1,798 research outputs found
Criticality and entanglement in random quantum systems
We review studies of entanglement entropy in systems with quenched
randomness, concentrating on universal behavior at strongly random quantum
critical points. The disorder-averaged entanglement entropy provides insight
into the quantum criticality of these systems and an understanding of their
relationship to non-random ("pure") quantum criticality. The entanglement near
many such critical points in one dimension shows a logarithmic divergence in
subsystem size, similar to that in the pure case but with a different universal
coefficient. Such universal coefficients are examples of universal critical
amplitudes in a random system. Possible measurements are reviewed along with
the one-particle entanglement scaling at certain Anderson localization
transitions. We also comment briefly on higher dimensions and challenges for
the future.Comment: Review article for the special issue "Entanglement entropy in
extended systems" in J. Phys.
Spectral statistics across the many-body localization transition
The many-body localization transition (MBLT) between ergodic and many-body
localized phase in disordered interacting systems is a subject of much recent
interest. Statistics of eigenenergies is known to be a powerful probe of
crossovers between ergodic and integrable systems in simpler examples of
quantum chaos. We consider the evolution of the spectral statistics across the
MBLT, starting with mapping to a Brownian motion process that analytically
relates the spectral properties to the statistics of matrix elements. We
demonstrate that the flow from Wigner-Dyson to Poisson statistics is a
two-stage process. First, fractal enhancement of matrix elements upon
approaching the MBLT from the metallic side produces an effective power-law
interaction between energy levels, and leads to a plasma model for level
statistics. At the second stage, the gas of eigenvalues has local interaction
and level statistics belongs to a semi-Poisson universality class. We verify
our findings numerically on the XXZ spin chain. We provide a microscopic
understanding of the level statistics across the MBLT and discuss implications
for the transition that are strong constraints on possible theories.Comment: 5 pages, 3 figure
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