Entanglement scaling of excited states in large one-dimensional many-body localized systems

Kennes, Dante M.; Karrasch, Christoph

doi:10.1103/physrevb.93.245129

Cited by 33 publications

(33 citation statements)

References 55 publications

(77 reference statements)

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“…The relatively small values of e 3 , even for the finite system sizes numerically available, make it possible to consider the input state as a very good approximation of an actual eigenstate ofH 3 to extend our study. We further note that contrary to recently proposed DMRGlike methods for excited states [40,49,[53][54][55][56][57][58] where the energy variance increases with the system size L, our method yields a power-law decaying σ[H, |Ψ 0 ] with L.…”

Section: Covariance Matrix and Hamiltonian Reconstructionmentioning

confidence: 56%

Many-body localization as a large family of localized ground states

Dupont

Laflorencie

2019

Phys. Rev. B

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Many-body localization (MBL) addresses the absence of thermalization in interacting quantum systems, with non-ergodic high-energy eigenstates behaving as ground states, only area-law entangled. However, computing highly excited many-body eigenstates using exact methods is very challenging. Instead, we show that one can address high-energy MBL physics using ground-state methods, which are much more amenable to many efficient algorithms. We find that a localized many-body ground state of a given interacting disordered Hamiltonian H0 is a very good approximation for a high-energy eigenstate of a parent Hamiltonian, close to H0 but more disordered. This construction relies on computing the covariance matrix, easily achieved using density-matrix renormalization group for disordered Heisenberg chains up to L = 256 sites. arXiv:1807.01313v2 [cond-mat.dis-nn]

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Section: Covariance Matrix and Hamiltonian Reconstructionmentioning

confidence: 56%

Many-body localization as a large family of localized ground states

Dupont

Laflorencie

2019

Phys. Rev. B

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“…Furthermore, we mapped out the mobility edge in this model, demonstrating that the method has a good energy resolution. Our criterion requires a sample of adjacent eigenstates in an energy window, and hence it can be straightforwardly evaluated by "spectral transformation" methods applicable to much larger system sizes, either via iterative diagonalizations [24] or DMRG [48][49][50][51].…”

Section: Discussionmentioning

confidence: 99%

Criterion for Many-Body Localization-Delocalization Phase Transition

2015

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We propose a new approach to probing ergodicity and its breakdown in one-dimensional quantum manybody systems based on their response to a local perturbation. We study the distribution of matrix elements of a local operator between the system's eigenstates, finding a qualitatively different behavior in the manybody localized (MBL) and ergodic phases. To characterize how strongly a local perturbation modifies the eigenstates, we introduce the parameter GðLÞ ¼ hlnðV nm =δÞi, which represents the disorder-averaged ratio of a typical matrix element of a local operator V to energy level spacing δ; this parameter is reminiscent of the Thouless conductance in the single-particle localization. We show that the parameter GðLÞ decreases with system size L in the MBL phase and grows in the ergodic phase. We surmise that the delocalization transition occurs when GðLÞ is independent of system size, GðLÞ ¼ G c ∼ 1. We illustrate our approach by studying the many-body localization transition and resolving the many-body mobility edge in a disordered one-dimensional XXZ spin-1=2 chain using exact diagonalization and time-evolving block-decimation methods. Our criterion for the MBL transition gives insights into microscopic details of transition. Its direct physical consequences, in particular, logarithmically slow transport at the transition and extensive entanglement entropy of the eigenstates, are consistent with recent renormalization-group predictions.

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“…This is partially due to a lack of methods to address this question. Tensor network methods [20][21][22] have been extended to be able to address properties of highly excited states, [23][24][25] prominently the DMRG-X method, 26 generalizing the density matrix renormalization group (DMRG) method 27 to capture highly excited states that feature an entanglement area-law.…”

Section: Introductionmentioning

confidence: 99%

Entanglement and spectra in topological many-body localized phases

et al. 2020

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Many-body localized systems in which interactions and disorder come together defy the expectations of quantum statistical mechanics: In contrast to ergodic systems, they do not thermalize when undergoing nonequilibrium dynamics. What is less clear, however, is how topological features interplay with many-body localized phases as well as the nature of the transition between a topological and a trivial state within the latter. In this work, we numerically address these questions, using a combination of extensive tensor network calculations, specifically DMRG-X, as well as exact diagonalization, leading to a comprehensive characterization of Hamiltonian spectra and eigenstate entanglement properties.

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Entanglement scaling of excited states in large one-dimensional many-body localized systems

Cited by 33 publications

References 55 publications

Many-body localization as a large family of localized ground states

Many-body localization as a large family of localized ground states

Criterion for Many-Body Localization-Delocalization Phase Transition

Entanglement and spectra in topological many-body localized phases

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