Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological interpretation of Luttinger theorem   Based solely on the analytical properties of the single-particle Green's
function of fermions at finite temperatures, we show that the generalized
Luttinger theorem inherently possesses topological aspects. The topological
interpretation of the generalized Luttinger theorem can be introduced because
i) the Luttinger volume is represented as the winding number of the
single-particle Green's function and thus ii) the deviation of the theorem,
expressed with a ratio between the interacting and noninteracting
single-particle Green's functions, is also represented as the winding number of
this ratio. The formulation based on the winding number naturally leads to two
types of the generalized Luttinger theorem. Exploring two examples of
single-band translationally invariant interacting electrons, i.e., simple metal
and Mott insulator, we show that the first type falls into the original
statement for Fermi liquids given by Luttinger, while the second type
corresponds to the extended one for non metallic cases with no Fermi surface
generalized by Dzyaloshinskii. This formulation also allows us to derive a
sufficient condition for the validity of the Luttinger theorem of the first
type by applying the Rouche's theorem in complex analysis as an inequality.
Moreover, we can rigorously prove in a non-perturbative manner, without
assuming any detail of a microscopic Hamiltonian, that the generalized
Luttinger theorem of both types is valid for generic interacting fermions as
long as the particle-hole symmetry is preserved. Finally, we show that the
winding number of the single-particle Green's function can also be associated
with the distribution function of quasiparticles, and therefore the number of
quasiparticles is equal to the Luttinger volume.

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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: math
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: q-bio