document: heavy - fermion systems @xcite are characterized by a hierarchy of distinctive energy scales @xcite . 
   the kondo scale , @xmath1 with bandwidth @xmath2 and superexchange @xmath3 , marks the screening of local magnetic moments . 
   this screening is a many - body effect which entangles the spins of the conduction electrons and local moments @xcite . below the coherence temperature , which is believed to track the kondo scale @xcite , the paramagnetic ( pm ) heavy - fermion liquid 
   @xcite emerges and corresponds to a coherent , bloch like , superposition of the screening clouds of the individual magnetic moments . even in the kondo limit , 
   where charge fluctuations of the impurity spins are completely suppressed , this paramagnetic state is characterized by a large fermi surface with luttinger volume including both the magnetic moments and conduction electrons @xcite . 
   the coherence temperature of this metallic state is small or , equivalently , the effective mass large . 
   + kondo screening competes with the ruderman - kittel - kasuya - yosida ( rkky ) interaction , which indirectly couples the local moments via the magnetic polarization of the conduction electrons . 
   the rkky energy scale is set by @xmath4 where @xmath5 corresponds to the spin susceptibility of the conduction electrons @xcite . 
   + the competition between kondo screening - favoring paramagnetic ground states - and the rkky interaction - favoring magnetically ordered states - is at the heart of quantum phase transitions @xcite , the detailed understanding of which is still under debate ( for recent reviews see ref . ) . + here , two radically different scenarios have been put forward to describe this quantum phase transition . in the _ standard _ hertz - millis picture @xcite , 
   the quasi - particles of the heavy - fermion liquid remain intact across the transition and undergo a spin - density wave transition . in particular , neutron scattering experiments of the heavy - fermion system @xmath6 
   show that fluctuations of the antiferromagnetic order parameter are responsible for the magnetic phase transition and that the transition is well understood in terms of the hertz - millis approach @xcite . 
   + on the other hand , since many experimental observations such as the almost wave vector independent spin susceptibility in @xmath7 @xcite , or the jump in the low - temperature hall coefficient in @xmath8 @xcite are not accounted for by this theory alternative scenarios have been put forward @xcite . in those scenarios , 
   the quantum critical point is linked to the very breakdown of the quasi - particle of the heavy - fermion state @xcite , and a topological reorganization of the fermi surface across the transition is expected @xcite . 
   + recent experiments on @xmath9 @xcite or @xmath10 @xcite show that a change in fermi surface ( fs ) topology must not necessarily occur only at the magnetic order - disorder quantum critical point ( qcp ) . 
   in fact , even in ybrh@xmath11si@xmath11 it has since been shown that the fermi surface reconstruction can be shifted to either side of the qcp via application of positive or negative chemical pressure @xcite .    in this paper , we address the above questions through an explicit calculation of the fermi surface topology in the framework of the kondo lattice model ( klm ) . in its simplest form 
   the klm describes an array of localized magnetic moments of spin @xmath12 , arising from atomic @xmath13-orbitals , that are coupled antiferromagnetically ( af ) via the exchange interaction @xmath3 to a metallic host of mobile conduction electrons . 
   + we present detailed dynamical cluster approximation ( dca ) calculations aimed at the investigation of the klm ground state . for the simulations within the magnetically ordered phase , 
   we have extended the dca to allow for symmetry breaking antiferromagnetic order . 
   we map out the magnetic phase diagram as a function of @xmath14 and conduction electron density @xmath15 , with particular interest in the single - particle spectral function and the evolution of the fermi surface . 
   the outline is as follows . 
   the model and the dca implementation is discussed in sec . 
   [ sec : section2 ] . 
   results for the case of half - band filling and hole - doping are discussed in sec . 
   [ sec : section3 ] and [ sec : section4 ] . 
   section  [ sec : section5 ] is devoted to a summary . 
   this paper is an extension to our previous work , where part of the results have already been published @xcite . 
   the kondo lattice model ( klm ) we consider reads @xmath16 the operator @xmath17 denotes creation of an electron in a bloch state with wave vector @xmath18 and a z - component of spin @xmath19 . 
   the spin @xmath12 degrees of freedom , coupled via @xmath20 , are represented with the aid of the pauli spin matrices @xmath21 by @xmath22 and the equivalent definition for @xmath23 using the localized orbital creation operators @xmath24 . 
   the chemical potential is denoted by @xmath25 . 
   the definition of the klm excludes charge fluctuations on the @xmath13-orbitals and as such a strict constraint of one electron per localized @xmath13-orbital has to be included . for an extensive review of this model we refer the reader to ref . . 
   + particle - hole symmetry at half - filling is given if hopping is restricted to nearest neighbors on the square lattice and the chemical potential is set to zero . 
   we introduce a next - nearest neighbor hopping with matrix element @xmath26 to give a modified dispersion @xmath27 -2 t ' \left [ \cos(k_{x}+k_{y } ) + \cos(k_{x}-k_{y})\right]$ ] . 
   as we will see , the suppression of particle - hole symmetry due to a finite value of @xmath26 leads to dramatic changes in the scaling of the quasi - particle gap at low values of @xmath14 and at half - band filling . 
   we have considered the value @xmath28 . 
   this choice guarantees that the spin susceptibility of the host metallic state at small dopings away from half - filling is peaked at wave vector @xmath29 . 
   thus , antiferromagnetic order as opposed to an incommensurate spin state is favored . 
   + to solve the model we have used the dca @xcite approach which retains _ temporal _ fluctuations and hence accounts for the kondo effect but neglects spatial fluctuations on a length scale larger than the cluster size . 
   the approach relies on the coarse - graining of momentum space , and momentum conservation holds only between the @xmath18-space patches . by gradually defining smaller sized patches the dca allows to restore the @xmath18-dependency of the self - energy . 
   + the standard formulation of dca is naturally translationally invariant . to measure orders beyond translation invariance 
   the dca can be generalized to lattices with a supercell containing @xmath30-unit cells of the original lattice @xcite . 
   a general unit cell is addressed by @xmath31 , @xmath32 denoting the supercell and @xmath33 the relative points with @xmath34 . in this work we opted for @xmath35 which is the minimum requirement for the formation of antiferromagnetic order . the reduced brillouin zone ( rbz ) 
   is then spanned by @xmath36 and @xmath37 and we have set the lattice constant to unity . 
   this supercell as well as the rbz ( also coined magnetic brillouin zone ( mbz ) ) are plotted in fig . 
   [ fig : fig1 ] . + the self - energy and green function are to be understood as spin dependent matrix functions , with an index for the unit cell within the supercell as well as an orbital index for the @xmath38- and @xmath13-orbitals in each unit cell . 
   the @xmath18-space discretization into @xmath39 patches with momentum conservation only between patches yields the coarse - grained lattice green function @xmath40 and ensures that the self - energy is only dependent on the coarse - grained momentum @xmath41 : @xmath42 . here 
   , the reciprocal vector @xmath43 denotes the center of a patch and the original @xmath18 vectors are given by @xmath44 . 
   the self - energy is extracted from a real - space cluster calculation with periodic boundaries yielding the quantized @xmath43 values . 
   let @xmath45 be the bath ( non - interacting ) green function of the cluster problem and @xmath46 the full cluster green function . 
   hence , @xmath47 and self - consistency requires that : @xmath48 +     and @xmath49 connect the af unit cells . 
   the two inequivalent @xmath38-orbitals are denoted by filled ( empty ) circles and the localized @xmath13-orbitals with arrows . 
   the reciprocal - space lattice vectors @xmath50 and @xmath51 span the magnetic brillouin zone . 
   the mbz is uniformly discretized in @xmath52 patches , corresponding to real - space clusters each containing @xmath39 magnetic unit cells . the color coding refers to constant momentum dependency of the self - energy and cluster green function . 
   the dashed square denotes the extended brillouin zone . ] 
   the non - interacting lattice green function is denoted by @xmath53 . 
   + to summarize , our implementation of dca approximates the fourier space of a lattice with two - point basis by patching . regarding the klm this leads to real - space clusters of size @xmath39 , each encompassing @xmath54 @xmath38- and @xmath13-orbitals . 
   in the present work cluster sizes @xmath55 and @xmath52 are considered ( fig . 
   [ fig : fig1 ] ) . 
   + the lattice green function @xmath56 with @xmath57 can equally be expressed as @xmath58 in an extended brillouin zone scheme , with @xmath59 and @xmath60 : @xmath61_{\mu \nu}\;. \label{eqn : eqn4}\end{aligned}\ ] ] in order to implement the dca one has to be able to solve , for a given bath , the kondo model on the effective cluster . 
   the method we have chosen is the auxiliary field quantum monte carlo ( qmc ) version of the hirsch - fye algorithm , following precisely the same realization as in ref . . 
   the implementation details of the self - consistency cycle can be found in ref . . 
   the performance of the qmc cluster solver has been enhanced by almost an order of magnitude by implementing the method of delayed updates @xcite . during the qmc markov process 
   the full updates of the green function are delayed until a sufficiently large number of local changes in the auxiliary field have been accumulated . 
   this enhances the performance of the whole qmc algorithm since considerable cpu time is spent in the updating section . to efficiently extract spectral information from the imaginary time discrete qmc data a stochastic analytic continuation scheme 
   is employed @xcite . 
   + ground state properties of the model are accessed by extrapolation of the inverse temperatures @xmath62 to infinity . 
   this is a demanding task since all relevant energy scales , the kondo scale , the coherence scale and the rkky scale , become dramatically smaller with decreasing @xmath14 . in the paramagnetic phase and below the coherence 
   scale a clear hybridization gap is apparent in the single particle spectral function and we use this criterion to estimate the coherence temperature . since the computational time required by the qmc cluster solver @xcite increases proportional to @xmath63 , this limits us in the resolution of energy scales to values of @xmath64 . 
   it is important to note that for small dopings away from half - band filling and for the considered cluster sizes , the negative sign problem is not severe and hence is not the limiting factor . 
   we consider the klm at half - filling in two cases : either with or without particle - hole symmetry . 
   that is @xmath65 and @xmath66 respectively . at @xmath67 lattice qmc simulations 
   do not suffer from the negative sign problem , and it is well established that the kondo screened phase gives way to an af ordered phase at @xmath68 @xcite . this magnetic order - disorder transition occurs between insulating states and it is reasonable to assume that it belongs to the three - dimensional @xmath69 universality class @xcite . here , the dynamical exponent takes the value of unity such that the correlation lengths in imaginary time and in real space are locked in together and diverge at the critical point . 
   due to the very small cluster sizes considered in the dca it is clear that we will not capture the physics of this transition . 
   in fact as soon as the correlation length exceeds the size of the dca cluster , symmetry breaking signaled by a finite value of the staggered moment @xmath70 sets in and mean - field exponents are expected . 
   the normalization is chosen such that the staggered magnetization of the fully polarized state takes the value of unity . the above quantity is plotted in fig . 
   [ fig : fig2 ] at @xmath65 and @xmath55 as apparent , the critical value of @xmath14 overestimates ( @xmath71 . ) 
   the _ exact _ lattice qmc result . 
   switching off nesting by including a finite value of @xmath72 shifts the magnetic order - disorder transition to lower values of @xmath14 . 
   + to improve on this result , we can systematically enhance the cluster size . however , our major interest lies in the single - particle spectral function . as we will see below , and well within the magnetically ordered phase , this quantity compares very well with the _ exact _ lattice qmc results .     of the local moment spins in the ground state as a function of coupling @xmath14 with next - nearest neighbor hopping @xmath73 and @xmath74 , respectively . 
   the low temperature limit is reached by performing simulations at various inverse temperatures @xmath62 . 
   convergence to the ground state has been achieved for the following inverse temperatures : @xmath75 ( @xmath76 ) , @xmath77 ( @xmath78 ) , @xmath79 ( @xmath80 ) and @xmath81 ( @xmath82 ) . ] 
   we have calculated the single - particle spectral function @xmath83 $ ] of the conduction electrons along a path of high symmetry in the extended brillouin zone . in all our spectral plots , on the energy axis , @xmath84 values are given relative to the chemical potential @xmath25 . 
   + in fig . 
   [ fig : fig3 ] we plot the spectrum for @xmath85 which was seen to be in the paramagnetic phase ( see fig . 
   [ fig : fig2 ] ) . 
   the lower band runs very flat around @xmath86 , with relatively low spectral weight ( note the logarithmic scale of the color chart ) in comparison to the other parts of the band which are mostly unchanged from the non - interacting case . 
   this feature is associated with kondo screening of the impurity spins and the resultant large effective mass of the composite quasi - particles . since no band crosses the fermi energy ( @xmath87 ) we classify this region of parameter space as a kondo insulator . 
   the observed dispersion relation is well described already in the framework of the large-@xmath88 mean - field theory of the kondo lattice model @xcite . at the particle - hole symmetric point 
   this approximation , which in contrast to the dca+qmc results of fig . 
   [ fig : fig3 ] neglects the constraint of no double occupancy of the @xmath13-orbitals , yields the dispersion relation of hybridized bands : @xmath89 . 
   \label{eqn : eqn6}\ ] ] within the mean - field theory the quasi - particle gap ( see eq . 
   [ eqn : eqn7 ] ) , @xmath90 , tracks the kondo scale . +     at half - filling ( @xmath91 ) and with particle - hole symmetry ( @xmath74 ) close to the magnetic phase transition on the paramagnetic side , @xmath85 . ]    at @xmath92 we have measured a non - vanishing staggered magnetization @xmath93 . the spectral function ( fig . 
   [ fig : fig4 ] ) for this lightly af ordered simulation now includes additional low - energy band structures : in the upper band around @xmath86 and in the lower band around @xmath94 . 
   these _ shadow bands _ arise due to the scattering of the heavy quasi - particle off the magnetic fluctuations centered at wave vector @xmath95 . +     at half - filling ( @xmath91 ) and with particle - hole symmetry ( @xmath74 ) close to the magnetic phase transition on the af side , @xmath92 ( a ) and closeup ( b ) . 
   the onset of magnetic order and concomitant emergence of the mbz is signaled by the appearance of shadow bands . 
   the staggered magnetization for this point is measured to be @xmath93 . ]    at @xmath96 we make a comparison with the spectrum obtained via qmc lattice simulations using the projective auxiliary field algorithm of ref . 
   for the same parameters . 
   we see in fig . 
   [ fig : fig5 ] the qmc lattice simulation results @xcite on the left and our dca result on the right , both only for the photoemission spectrum @xmath97 . 
   the agreement of the dca spectrum with the blankenbecler - scalapino - sugar ( bss ) result is excellent . as in the bss lattice calculations and for the particle - hole symmetric case , the conduction ( valence ) band maximum ( minimum ) 
   is located at @xmath98 ( @xmath99 ) for all considered values of @xmath14 . 
   +     with the @xmath100 spectral function . data ( a ) taken from ref . 
   which used a projective auxiliary field monte carlo ( bss ) method for the klm on a @xmath101 lattice and our dca results ( b ) at @xmath77 , both for the same parameter set - @xmath74 , @xmath102 , @xmath96.,title="fig : " ] +    it is noteworthy that already with the smallest possible cluster capable of capturing af order , @xmath55 , we are able to produce a single - particle spectrum which is essentially the same as the lattice qmc result . 
   this confirms that the dca is indeed a well suited approximation for use with the klm : the essence of the competition between rkky - mediated spacial magnetic order and the time - displaced correlations responsible for kondo screening is successfully distilled to a small cluster dynamically embedded in the mean - field of the remaining bath electrons . 
   we now set @xmath73 , but remain at half - filling via careful adjustment of the chemical potential @xmath25 . with decreasing @xmath14 we can divide the phase diagram into four regions on the basis of the characteristic spectrum in each region . for @xmath103 ( fig . 
   [ fig : fig6](a ) ) the spectrum is qualitatively identical to the pm phase in the @xmath74 case such that the model is a kondo insulator with an indirect gap . 
   the minimum of the valence band lies at @xmath94 and the maximum of the conduction band is at @xmath86 . 
   + for @xmath104 ( fig . 
   [ fig : fig6](b ) ) the system is weakly af ordered , and the spectrum reflects this in the development of shadow bands , but is otherwise qualitatively the same as before . at @xmath105 ( fig . 
   [ fig : fig6](c ) ) , well inside the af phase , the shadow bands are more pronounced and now the minimum of the valence band has shifted to @xmath106 . the final plot in the series ( fig . 
   [ fig : fig6](d ) ) , with @xmath107 shows that the form of the lower band has also changed such that the maximum of this band now lies at @xmath108 . 
   + in figs . 
   [ fig : fig7](a - h ) we show the evolution of this lower band between @xmath94 and @xmath86 with an enlargement of the energy axis around the fermi energy . 
   the local minimum energy dip at @xmath108 becomes less pronounced as the heavy - fermion band flattens until by the time we reach @xmath96 this dip has turned into a bump such that the lower band maximum has shifted from @xmath86 to @xmath108 . 
   this important change in band structure appears to be continuous . for smaller coupling , @xmath109 , @xmath110 , and @xmath111 
   the lower band maximum remains at @xmath108 and becomes more pronounced . 
   assuming a rigid band picture , this evolution of the band structure maps onto a topology change of the fermi surface at small dopings away from half filling . 
   we will see by explicit calculations at finite dopings that this topology change indeed occurs . 
   + the position of the minima and maxima in the valence and conduction bands of the spectra for @xmath73 are summarized schematically in fig . 
   [ fig : fig8 ] .     and for half - filling . 
   the squares represent the first brillouin zone ( for the pm phase ) or the extended brillouin zone ( for the af phase ) , with the bottom left corner and top right corner of each square given by @xmath112 and @xmath86 , respectively.,title="fig : " ] +      the quasi - particle gap corresponds to the energy difference between the top of the conduction band and the bottom of the valence band . to be more precise , @xmath113 here , @xmath114 corresponds to the ground state energy of the @xmath115 particle system with total momentum @xmath18 and @xmath116 . 
   technically , the energy differences are at best extracted from the low temperature single - particle green functions : @xmath117     as a function of kondo coupling @xmath14 . at @xmath118 , the magnetic order - disorder transition takes place at @xmath119 . in the coupling range @xmath120 kondo screening coexists with magnetism and is at the origin of the quasiparticle gap . ]    in the large @xmath14 limit , each impurity spin traps a conduction electron in a kondo singlet . 
   the wave function corresponds to a direct product of such kondo singlets and the quasi - particle gap is set by the energy scale @xmath121 required to break a kondo singlet . 
   hence , in the large @xmath14 limit the quasi - particle gap does not depend on the details of the band structure . 
   the situation is more subtle in the weak - coupling limit , where the underlying nesting properties of the fermi surface play a crucial role . assuming static impurity spins locked into an antiferromagnetic order , @xmath122 one obtains the single particle dispersion relation @xmath123 with @xmath124 . in one dimension and at @xmath74 
   nesting leads to @xmath125 and magnetic order opens a quasi - particle gap set by @xmath126 . 
   both the dca results presented in fig . [ 
   fig : fig9 ] as well as the bss results of ref . 
   support this point of view . in one - dimension , 
   this scaling of the quasi - particle gap is also observed @xcite . at @xmath66 nesting 
   is not present and magnetic ordering can only partially gap the fermi surface . since the dca results of fig . 
   ( [ fig : fig9 ] ) support a finite quasi - particle gap in the magnetically ordered phase , the above frozen - spin ansatz fails and points to one of the main result of our work , namely that within the magnetically ordered phase kondo screening and the heavy quasi - particles are still present . 
   even though we can not track the functional form of the gap at @xmath127 and at weak couplings , we interpret the dca results in terms of a quasi - particle gap which tracks the kondo scale from weak to strong coupling as in the large-@xmath88 mean - field calculations @xcite . 
   in this section we concentrate on the hole - doped klm at @xmath66 . 
   we will first map out the magnetic phase diagram in the doping versus coupling plane and then study the evolution of single - particle spectral function from the previously discussed half - filled case to the heavily doped paramagnetic heavy - fermion metallic state .       of the @xmath13-electrons as a function of @xmath15 at different constant couplings @xmath14 . ] 
   [ fig : fig10 ] shows the staggered magnetization as a function of conduction electron density for @xmath82 , @xmath110 , @xmath128 and @xmath129 . 
   the magnetically ordered state found at half - filling initially survives when doping with holes . at all coupling values a continuous magnetic phase transition 
   is observed with the af order decreasing gradually as the system is doped and vanishing smoothly at a quantum critical point . 
   the results are summarized in the magnetic phase diagram shown in fig . 
   [ fig : fig11 ] . 
   with decreasing values of @xmath14 and increasing dopings the rkky interaction progressively dominates over the kondo scale and the magnetic metallic state is stabilized . 
   checks were made by varying the temperature , @xmath130 , of the simulations to ensure that the results can be considered to be ground state . 
   below @xmath131 we found the coherence scale to be too low to guarantee convergence . 
   as pointed out previously , the limiting computational factor is the cubic scaling of the hirsch - fye @xcite algorithm , @xmath132 and not the negative sign problem . 
   ( color - coded ) as a function of coupling @xmath14 and conduction electron occupancy @xmath15 . 
   triangles : pm region , large fs . 
   squares : af , large fs . circles : af , small fs . here @xmath66 and the calculations 
   are carried out with the @xmath133 cluster . 
   below , the fs topologies corresponding to the numbered regions are shown schematically.,title="fig : " ] +      we have calculated and followed the evolution of the single - particle spectrum , plotted in an extended brillouin zone scheme . to begin with we set @xmath80 and show results in fig . 
   [ fig : fig12 ] for the spectral function , as it is here that a change in the fermi surface topology becomes evident . 
   starting from the previously discussed half - filled case ( fig . 
   [ fig : fig12](a ) ) a rigid band approximation produces hole pockets around the @xmath134 points in the brillouin zone . 
   this is confirmed by explicit calculations at small dopings away from half - filling as demonstrated in fig . 
   [ fig : fig12](b ) . with further doping 
   this low energy band flattens out progressively becoming almost flat by @xmath135 ( fig . 
   [ fig : fig12](d ) ) . 
   doping further gives rise to a fermi surface with holes centered around @xmath136 . 
   since at @xmath137 ( fig . 
   [ fig : fig12](e ) ) and @xmath138 ( fig . 
   [ fig : fig12](f ) ) we still have non - zero magnetizations of @xmath139 and @xmath140 , respectively , shadow features centered around @xmath94 are expected . 
   the weight of those shadow features progressively diminishes as the staggered magnetization vanishes . 
   in particular , in fig .  [ 
   fig : fig12](g ) the magnetization is very small ( @xmath141 ) and indistinguishable from zero in the final figure of the series . + across the transition from @xmath142 to @xmath143 the quasiparticle weight @xmath144 as obtained from the behaviour of @xmath145 at large imaginary times decreases albeit it shows no sign of singularity . 
   this observation stands in agreement with results obtained at half - band filling @xcite and excludes the occurrence of a kondo breakdown . + 
   this evolution of the single - particle spectral function at @xmath146 points to three distinct fermi surface topologies , sketched in fig . 
   [ fig : fig11 ] . in the paramagnetic phase ( fermi surface ( 1 ) in fig . 
   [ fig : fig11 ] ) the fermi surface consists of hole pockets around the @xmath147 points in the brillouin zone . 
   even though in our simulations charge fluctuations of the @xmath13-sites are completely prohibited , the fermi surface volume accounts for both the conduction electrons and impurity spins . 
   this fermi surface topology maps onto that of the corresponding non - interacting periodic anderson model with total particle density given by @xmath148 and is coined large fermi surface . in the antiferromagnetic metallic phase close to the magnetic order - disorder transition , ( fermi surface ( 2 ) in fig . 
   [ fig : fig11 ] ) the fermi surface merely corresponds to a backfolding of the paramagnetic fermi surface as expected in a generic spin - density wave transition . here 
   , a heavy quasi - particle with crystal momentum @xmath18 can scatter off a magnon with momentum @xmath149 to produce a shadow feature at @xmath150 . 
   it is only within the magnetically ordered phase that we observe the topology change of the fermi surface to hole pockets centered around @xmath151 . due to the antiferromagnetic order and the accompanied reduced brillouin zone 
   , this fermi surface topology satisfies the luttinger sum rule . 
   we coin it a small fermi surface in the sense that it is linked to that obtained in a frozen @xmath13-spin mean - field calculation as presented in eq . 
   ( [ eqn : eqn9 ] ) .     of the conduction electrons for @xmath105 and @xmath73 , at @xmath152 . 
   the shadow features present in ( a ) vanish as the occupation number @xmath15 is reduced . ] 
   we have equally plotted the single - particle spectral function at higher values of @xmath105 as a function of doping ( see fig . [ 
   fig : fig13 ] ) . for this coupling strength , and at half - band filling , 
   the conduction band maximum is located at @xmath86 with accompanying shadow bands at @xmath94 . 
   the fermi surface obtained upon doping follows from a rigid band approximation , and yields the topology shown in fig . 
   [ fig : fig11 ] ( 2 ) . 
   the transition to the paramagnetic state shows up in the vanishing of the shadow features at @xmath153 . 
   + we note that our results are confirmed by simulations carried out using the larger cluster size @xmath52 , see fig . 
   [ fig : fig14 ] . 
   in particular , we observe the small fermi surface topology in the strong af region with small coupling @xmath14 and evidence for a large fermi surface in the weakly ordered region ( @xmath154 ) .     of the conduction electrons obtained using cluster size @xmath52 . confirming that the small fermi surface topology in the lightly doped af phase with coupling @xmath80 is not an artifact of the smaller cluster results . 
   the staggered magnetisation of the @xmath13-electrons is @xmath155 . ] 
   we resort to a mean - field modelling in order to propose a scenario for the detailed nature of the topological transition of the fs within the ordered phase . within this model 
   the topology change will correspond to two lifshitz transitions . 
   aspects of the single - particle spectral function can be well accounted for within the following mean - field hamiltonian @xcite : @xmath156 here @xmath157 , ( @xmath25 ) are lagrange multipliers fixing the @xmath13- ( @xmath38- ) particle number to unity ( @xmath15 ) and @xmath158 , @xmath159 corresponds to the staggered magnetization of the conduction and @xmath13-electrons . 
   the order parameter for kondo screening is @xmath160 . 
   the large-@xmath88 mean - field saddle point corresponds to the choice @xmath161 and @xmath162 . 
   as already mentioned this saddle point gives a good account of the hybridized bands we observe numerically in the paramagnetic phase . in the magnetic phase 
   , one could speculate that kondo screening breaks down such that the @xmath13-spins are frozen and do not participate in the luttinger volume . 
   this corresponds to the parameter set @xmath163 , @xmath164 and @xmath165 and leads to the dispersion relation of eq . 
   ( [ eqn : eqn8 ] ) . throughout the phase diagram of fig . 
   [ fig : fig11 ] the single - particle spectral function never shows features following this scenario . in fact , many aspects of the spectral function in the magnetically ordered phase can be understood by choosing @xmath166 , @xmath167 and @xmath168 . 
   this explicitly accounts for a heavy - fermion band in the ordered phase . 
   it is in this sense that we claim the absence of kondo breakdown within our model calculations . 
   [ fig : fig15 ] plots the four - band energy dispersion relation @xmath169 obtained from the mean - field calculation in the magnetically ordered phase at @xmath73 , @xmath80 and at band fillings @xmath170 ( fig . 
   [ fig : fig15](a , b ) ) and @xmath171 ( fig . 
   [ fig : fig15](c , d ) ) corresponding to the fermi surface topologies labeled ( 2 ) and ( 3 ) , respectively , in fig . 
   [ fig : fig11 ] . in each case 
   we have used the dca value for the magnetization and varied @xmath172 to obtain the best qualitative fit to the respective dca spectrum . 
   the change in the topology of the fermi surface stems from a delicate interplay of the relative magnitudes of the magnetization @xmath173 and _ kondo screening _ 
   parameter @xmath172 . +     with @xmath80 ( @xmath73 ) . 
   ( a ) @xmath174 , @xmath170 . 
   the line intensity is proportional to the quasi - particle spectral weight , @xmath175 . 
   the fermi surface topology ( see closeup ( b ) ) results from backfolding of the large-@xmath88 mean - field bands . 
   this corresponds to the fermi surface ( 2 ) in fig.[fig : fig11 ] . 
   + ( d ) @xmath176 , @xmath171 . 
   the fermi surface topology ( see closeup ( c ) ) corresponds to that of hole pockets centered around @xmath177 as depicted by the fermi surface ( 3 ) in fig . 
   [ fig : fig11 ] . ]    in the dca calculations , we are unable to study the precise nature of the topology change of the fermi surface within the magnetically ordered phase since the energy scales are too small . 
   however we can draw on the mean - field model to gain some insight . 
   [ fig : fig16 ] plots the dispersion relation along the @xmath94 to @xmath86 line in the brillouin zone as a function of @xmath172 . 
   we would like to emphasize the following points . 
   i ) the transition from hole pockets around the wave vector @xmath178 to @xmath179 corresponds to two lifshitz transitions in which the hole pockets around @xmath178 disappears and those around @xmath180 emerge . 
   the luttinger sum rule requires an intermediate phase with the presence of pockets both at @xmath180 and at @xmath178 . 
   this situation is explicitly seen in fig . 
   [ fig : fig16](b ) at @xmath181 . 
   ii ) starting from the antiferromagnetic state with hole pockets at @xmath177 there is an overall flatting of the band prior to the change in the fermi surface topology . 
   hence on both sides of the transition , an enhanced effective mass is expected . owing to point i ) 
   the effective mass does not diverge . 
   iii ) the two lifshitz transition scenario suggested by this mean - field modeling , leads to a continuous change of the hall coefficient . however , since a very _ small _ variation of the hybridization @xmath172 suffices to change the fermi surface topology one can expect , as a function of this control parameter , a rapid variation of the hall coefficient as it is observed in experiment @xcite .     of the dca results ( @xmath80 , @xmath73 @xmath182 , @xmath183 , @xmath170 ) . 
   as apparent on the scale of the closeup ( b ) , hole pockets around @xmath180 as well as around @xmath178 are present at @xmath184 . ] 
   the evolution of the fermi surface across the magnetic order - disorder transition has been investigated by other groups and especially in the framework of a gutzwiller projected mean - field wave function corresponding to the ground state of the single particle hamiltonian of eq . 
   [ eqn : eqn9 ] . both a variational quantum monte carlo calculation @xcite as well as a gutzwiller approximation @xcite show a rich phase diagram which bears some similarities but also important differences with the present dca calculation . at small doping away from half - filling , 
   the magnetic transition as a function of the coupling @xmath14 is continuous and of sdw type as marked by the back - folding of the fermi surface . within the magnetically ordered phase a first order transition occurs between hole ( af@xmath185 ) and electron ( af@xmath186 ) like fermi surfaces . at larger hole dopings , 
   the magnetic transition is of first order and the fermi surface abruptly changes from large to small ( af@xmath186 ) . 
   the calculations in refs .   are carried out at @xmath187 . at finite values of @xmath188 
   one expects the af@xmath186 fermi - surface topology to correspond to hole pockets centered around @xmath189 as shown in fig . 
   [ fig : fig12 ] . on the other hand , 
   the af@xmath185 fermi surface arises from a back - folding of the large fermi surface ( fig . 
   [ fig : fig13 ] ) . with this identification , 
   our dca results bear some similarity with the variational calculation in the sense that the same fermi surface topologies are realized . 
   however , in our calculations we see no sign of first order transitions and no direct transitions from the large paramagnetic fermi - surface topology to the af@xmath186 phase . 
   it is equally important to note that in both the variational and dca approaches no kondo breakdown is apparent . 
   in particular the variational parameter @xmath190 which encodes hybridization between the @xmath13- and @xmath38-electrons never vanishes @xcite . on the other hand , @xmath100 cdmft calculations of the three - dimensional periodic anderson model on a two site cluster and finite sized baths @xcite have put forward the idea that the magnetic order - disorder transition is driven by an orbital selective mott transition or in other words a kondo breakdown @xcite . 
   in particular even in the presence of spin symmetry broken baths allowing for antiferromagnetic ordering a big enhancement of the @xmath13-effective mass is apparent in the vicinity of the magnetic transition . in the paramagnetic phase , 
   the low energy decoupling of the @xmath13- and @xmath38-electrons stem from the vanishing of the hybridization function at low energies . 
   our results , which makes no approximation of the number of bath degrees of freedom and which allow to treat larger cluster sizes do not support this point of view . 
   in particular as shown in ref . 
   no singularity in the quasiparticle weight is apparent across the transition . 
   equally , fig . 
   [ fig : fig12 ] which plots the single particle spectral function at finite doping shows no singularity in @xmath191 . 
   we have presented detailed dca+qmc results for the kondo lattice model on a square lattice . 
   our dca approach allows for antiferromagnetic order such that spectral functions can be computed across magnetic transitions and in magnetically ordered phases . at the particle - hole symmetric point ( half - band filling and @xmath67 ) 
   we can compare this approach to previous _ 
   lattice qmc auxiliary field simulations @xcite . 
   unsurprisingly , with the _ small _ cluster sizes considered in the dca approach the critical value of @xmath14 at which the magnetic order - disorder transition occurs is substantially overestimated . 
   the important point however is that the dca+qmc approximation gives an extremely good account of the single - particle spectral function both in the paramagnetic and antiferromagnetic phases . 
   hence , and as far as we can test against benchmark results , the combination of static magnetic ordering and dynamical kondo screening , as realized in the dca , provides a very good approximation of the underlying physics . + as opposed to _ exact _ 
   lattice qmc auxiliary field simulations , which fail away from the particle - hole symmetric point due to the so - called negative sign problem , the dca+qmc approach allows us to take steps away from this symmetry either by doping or by introducing a finite value of @xmath26 . 
   it is worthwhile noting that for cluster sizes up to @xmath0 orbitals the limiting factor is the cubic scaling of the hirsch - fye algorithm rather than the negative sign problem which turns out to be very mild in the considered parameter range . 
   + our major findings are summarized by the following points . 
   + i ) we observe no kondo breakdown throughout the phase diagram even deep in the antiferromagnetic ordered state where the staggered magnetization takes large values . 
   this has the most dramatic effect at half - band filling away from the particle - hole symmetric point and at small values of @xmath14 where magnetic order is robust . here 
   , magnetism alone will not account for the insulating state and the observed quasi - particle gap can only be interpreted in terms of kondo screening . 
   the absence of kondo breakdown throughout the phase diagram is equally confirmed by the single - particle spectral function which always shows a feature reminiscent of the heavy - fermion band.@xcite + ii ) the transition from the paramagnetic to the antiferromagnetic state is continuous and is associated with the backfolding of the large heavy fermion fermi surface . 
   + iii ) within the antiferromagnetic metallic phase there is a fermi surface topology change from hole pockets centered around @xmath86 at _ small _ values of the magnetization @xmath159 to one centered around @xmath192 at _ larger _ values of @xmath159 . 
   the latter fermi surface is adiabatically connected to one where the @xmath13-spins are frozen and in which kondo screening is completely absent . 
   @xcite this transition comes about by _ continuously deforming 
   _ a heavy - fermion band such that the effective mass grows substantially on both sides of the transition . within a mean - field modelling of the quantum monte carlo 
   results the transition in the fermi surface topology corresponds to two continuous lifshitz transitions . as a function of decreasing mean - field kondo screening parameter @xmath172 and at constant hole doping , the volume of the hole pocket at @xmath86 decreases at the expense of the increase of volume of the hole pocket at @xmath108 . 
   owing to the luttinger sum rule , the total volume of the hole pockets remains constant . 
   it is important to note that the energy scales required to resolve the nature of this transition are presently orders of magnitudes smaller than accessible within the dca with a quantum monte carlo solver . 
   +   + we would like to thank the dfg for financial support under the grant numbers as120/6 - 1 ( for1162 ) and as120/4 - 3 . 
   the numerical calculations were carried out at the lrz - munich as well as at the jsc - jlich . 
   we thank those institutions for generous allocation of cpu time .
summary: we report the results of extensive dynamical cluster approximation calculations , based on a quantum monte carlo solver , for the two - dimensional kondo lattice model . 
   our particular cluster implementation renders possible the simulation of spontaneous antiferromagnetic symmetry breaking . by explicitly computing the single - particle spectral function both in the paramagnetic and antiferromagnetic phases 
   , we follow the evolution of the fermi surface across this magnetic transition . 
   the results , computed for clusters up to @xmath0 orbitals , show clear evidence for the existence of three distinct fermi surface topologies . 
   the transition from the paramagnetic metallic phase to the antiferromagnetic metal is continuous ; kondo screening does not break down and we observe a back - folding of the paramagnetic heavy fermion band . within the antiferromagnetic phase and 
   when the ordered moment becomes _ large _ the fermi surface evolves to one which is adiabatically connected to a fermi surface where the local moments are frozen in an antiferromagnetic order .