Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nature of Many-Body Localization and Transitions by Density Matrix
  Renormaliztion Group and Exact Diagonalization Studies   A many-body localized (MBL) state is a new state of matter emerging in a
disordered interacting system at high energy densities through a disorder
driven dynamic phase transition. The nature of the phase transition and the
evolution of the MBL phase near the transition are the focus of intense
theoretical studies with open issues in the field. We develop an entanglement
density matrix renormalization group (En-DMRG) algorithm to accurately target
the entanglement patterns of highly excited states for MBL systems. By studying
the one dimensional Heisenberg spin chain in a random field, we demonstrate the
high accuracy of the method in obtaining statistical results of quantum states
in the MBL phase. Based on large system simulations by En-DMRG for excited
states, we demonstrate some interesting features in the entanglement entropy
distribution function, which is characterized by two peaks; one at zero and
another one at the quantized entropy $S=ln2$ with an exponential decay tail on
the $S>ln2$ side. Combining En-DMRG with exact diagonalization simulations, we
demonstrate that the transition from the MBL phase to the delocalized ergodic
phase is driven by rare events where the locally entangled spin pairs develop
long-range power-law correlations. The corresponding phase diagram contains an
intermediate regime, which has power-law spin-z correlations resulting from
contributions of the rare events. We discuss the physical picture for the
numerical observations in the intermediate regime, where various distribution
functions are distinctly different from results deep in the ergodic and MBL
phases for finite-size systems. Our results may provide new insights for
understanding the phase transition in such systems.

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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas