Return probability for the Anderson model on the random regular graph

Bera, Soumya; Tomasi, Giuseppe De; Khaymovich, Ivan M.; Scardicchio, Antonello

doi:10.1103/physrevb.98.134205

Cited by 81 publications

(54 citation statements)

References 72 publications

(135 reference statements)

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“…First, we computed the time dependent spin-spin correlator and extracted the exponents θ and η that determine the relaxation time, τ , and the spin-glass order parameter. Comparing the numerical results with analytical expectations we conclude that both τ and q EA display exponential dependencies on the system size n as expected (10,11) in the whole non-ergodic phase. The exponents controlling these dependencies are very close to the expected values at energies away from localization transition.…”

Section: Matrix Elements: Analytic Derivation and Numerical Resultssupporting

confidence: 65%

Non-ergodic extended phase of the Quantum Random Energy model

2019

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The concept of non-ergodicity in quantum many body systems can be discussed in the context of the wave functions of the many body system or as a property of the dynamical observables, such as time-dependent spin correlators. In the former approach the non-ergodic delocalized states is defined as the one in which the wave functions occupy a volume that scales as a non-trivial power of the full phase space. In this work we study the simplest spin glass model and find that in the delocalized non-ergodic regime the spin-spin correlators decay with the characteristic time that scales as non-trivial power of the full Hilbert space volume. The long time limit of this correlator also scales as a power of the full Hilbert space volume. We identify this phase with the glass phase whilst the many body localized phase corresponds to a 'hyperglass' in which dynamics is practically absent. We discuss the implications of these finding to quantum information problems. arXiv:1812.06016v2 [cond-mat.dis-nn]

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Section: Matrix Elements: Analytic Derivation and Numerical Resultssupporting

confidence: 65%

Non-ergodic extended phase of the Quantum Random Energy model

2019

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“…Finally, a significant contingent agrees with the three-regime phase diagram presented in this work, at least under the correct conditions. [49,63,66,84] We hope our relatively elementary flow approach and resulting intuitive picture of the three-phase proposal has a clarifying effect on this confusing situation.…”

Section: Review Of Previous Resultsmentioning

confidence: 99%

Anderson localization on the Bethe lattice using cages and the Wegner flow

2019

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Anderson localization on tree-like graphs such as the Bethe lattice, Cayley tree, or random regular graphs has attracted attention due to its apparent mathematical tractability, hypothesized connections to many-body localization, and the possibility of non-ergodic extended regimes. This behavior has been conjectured to also appear in many-body localization as a "bad metal" phase, and constitutes an intermediate possibility between the extremes of ergodic quantum chaos and integrable localization. Despite decades of research, a complete consensus understanding of this model remains elusive. Here, we use cages, maximally tree-like structures from extremal graph theory; and numerical continuous unitary Wegner flows of the Anderson Hamiltonian to develop an intuitive picture which, after extrapolating to the infinite Bethe lattice, appears to capture ergodic, non-ergodic extended, and fully localized behavior.Physical Review B 100, 094201 (2019).

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“…[49,50] and discussed in detail in [50]) and in real many-body systems [51,52]. Slow dynamics on RRG [53][54][55] and in disordered spin chains [56][57][58] may be a signature of such a phase. In this work we suggest the translation-invariant extension of the RP model and study the localization properties of the RP family of models along with the PLRBM family as the correlations in the long-range hopping increase.…”

Section: Introductionmentioning

confidence: 99%

Correlation-induced localization

2019

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A new paradigm of Anderson localization caused by correlations in the long-range hopping along with uncorrelated on-site disorder is considered which requires a more precise formulation of the basic localizationdelocalization principles. A new class of random Hamiltonians with translation-invariant hopping integrals is suggested and the localization properties of such models are established both in the coordinate and in the momentum spaces alongside with the corresponding level statistics. Duality of translation-invariant models in the momentum and coordinate space is uncovered and exploited to find a full localization-delocalization phase diagram for such models. The crucial role of the spectral properties of hopping matrix is established and a new matrix inversion trick is suggested to generate a one-parameter family of equivalent localization/delocalization problems. Optimization over the free parameter in such a transformation together with the localization/delocalization principles allows to establish exact bounds for the localized and ergodic states in long-range hopping models. When applied to the random matrix models with deterministic power-law hopping this transformation allows to confirm localization of states at all values of the exponent in power-law hopping and to prove analytically the symmetry of the exponent in the power-law localized wave functions.

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Return probability for the Anderson model on the random regular graph

Cited by 81 publications

References 72 publications

Non-ergodic extended phase of the Quantum Random Energy model

Non-ergodic extended phase of the Quantum Random Energy model

Anderson localization on the Bethe lattice using cages and the Wegner flow

Correlation-induced localization

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