Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Annalen der Physik

Signature of non‐ergodicity in low‐lying excitations of disordered many‐particle systems

Richard Berkovits

Published Apr 27, 2017• 5 citations
Publisher

Abstract

Statistical properties of the low‐lying states of the entanglement spectrum of a one‐dimensional interacting disordered system are studied in order to understand the localized to extended transition as function of interaction strength and excitation number expected from the many‐body localization transition. It is shown that such a transition is observed in the statistics of the level‐spacing of the entanglement spectrum. For an intermediate range of excitation numbers and strong interaction strength where the entanglement spectrum shows a clear extended behavior, a signature of non‐ergodic behavior also emerges. We interpret this as evidence for a non‐ergodic‐extended phase suggested by previous studies.

DOI
10.1002/andp.201700042

Related papers

Signature of the many-particle localization transition in the entanglement spectrum

Richard Berkovits

We use the statistical properties of the entanglement spectrum of an interacting disordered system, in order to track the localized to extended transition as function of interaction strength and excitation energy expected from the many-body localization transition. We show that such a transition is indeed observed, although an interesting saturation behavior in the intermediate excitation energy is seen.

Journal of Physics Conference Series•Mar 1, 2016•2 citations

Entanglement entropy of low-lying excitation in localized interacting system: Signature of Fock space delocalization

Richard Berkovits

The properties of the entanglement entropy (EE) of low-lying excitations in one-dimensional disordered interacting systems are studied. The ground state EE shows a clear signature of localization, while low-lying excitations show a significantly longer localization length. The dependence of the localization as a function of interaction strength and sample length is studied using the density matrix renormalization group (DMRG). This behavior corresponds to the presence of the predicted many-particle critical energy in the vicinity of the ground state energy. The implications of these results on experiments are discussed.

arXiv:1310.1556•Physical Review B•May 30, 2014•11 citations

Low eigenvalues of the entanglement Hamiltonian, localization length, and rare regions in one-dimensional disordered interacting systems

Richard Berkovits

The properties of the low-lying eigenvalues of the entanglement Hamiltonian and their relation to the localization length of a disordered interacting one-dimensional many-particle system are studied. The average of the first entanglement Hamiltonian level spacing is proportional to the ground-state localization length and shows the same dependence on the disorder and interaction strength as the localization length. This is the result of the fact that entanglement is limited to distances of order of the localization length. The distribution of the first entanglement level spacing shows a Gaussian-type behavior as expected for level spacings much larger than the disorder broadening. For weakly disordered systems (localization length larger than sample length), the distribution shows an additional peak at low-level spacings. This stems from rare regions in some samples which exhibit metalliclike behavior of large entanglement and large particle-number fluctuations. These intermediate microemulsion metallic regions embedded in the insulating phase are discussed.

arXiv:1710.01546•Physical review. B./Physical review. B•Mar 8, 2018•6 citations

Correspondence between many-particle excitations and the entanglement spectrum of disordered ballistic one-dimensional systems

Shaul Leiman, Ariel Eisenbach, Richard Berkovits

Using exact diagonalization for non-interacting systems and density matrix renormalization group for interacting systems we show that Li and Haldane's conjecture on the correspondence between the low-lying many-particle excitation spectrum and the entanglement spectrum holds for disordered ballistic one-dimensional many-particle systems. In order to demonstrate the correspondence we develop a computationally efficient way to calculate the entanglement spectrum of low-lying excitation of non-interacting systems. We observe and explain the presence of an unexpected shell structure in the excitation spectrum. The low-lying shells are robust and survive even for strong electron-electron interactions.

arXiv:1507.06177•Europhysics Letters (EPL)•Nov 1, 2015•7 citations

Ergodic and non-ergodic properties of disordered SU(3) chains

Bhupen Dabholkar, Fabien Alet

Non-abelian symmetries are thought to be incompatible with many-body localization, but have been argued to produce in certain disordered systems a broad non-ergodic regime distinct from many-body localization. In this context, we present a numerical study of properties of highly-excited eigenstates of disordered chains with SU(3) symmetry. We find that while weakly disordered systems rapidly thermalize, strongly-disordered systems indeed exhibit non-thermal signatures over a large range of system sizes, similar to the one found in previously studied SU(2) systems. Our analysis is based on the spectral, entanglement, and thermalization properties of eigenstates obtained through large-scale exact diagonalization exploiting the full SU(3) symmetry.

arXiv:2403.00442•Mar 1, 2024•0 citations

Many-body localization identified by entanglement in momentum space

Bingtian Ye, Zhaoyu Han, Liang-Zhu Mu +1 more

We study the entanglement in momentum space of a disordered one-dimensional fermion lattice model with attractive interaction. We observe that the many-body localization transition can be characterized by behaviors of two components in entanglement spectrum. One of the components is related to paired-fermion entanglement which contributes to the long-range correlation in position space, and the vanishing of it indicates the emerged many-body localized phase. Based on this understanding, we identify the critical point between delocalized and localized phases for interaction of different strength. Additionally by method of entanglement spectrum, we provide a new evidence to show the transition of two phases induced by interaction, and find this phase transition is not influenced by the disorder. Our result shows key characteristics in entanglement for different phases in the system, and provides a novel perspective to understand many-body localization phenomenon.

•Jul 20, 2016•0 citations
Statistical properties of the low‐lying states of the entanglement spectrum of a one‐dimensional interacting disordered system are studied in order to understand the localized to extended transition as function of interaction strength and excitation number expected from the many‐body localization transition. It is shown that such a transition is observed in the statistics of the level‐spacing of the entanglement spectrum. For an intermediate range of excitation numbers and strong interaction strength where the entanglement spectrum shows a clear extended behavior, a signature of non‐ergodic behavior also emerges. We interpret this as evidence for a non‐ergodic‐extended phase suggested by previous studies.
The properties of the entanglement entropy (EE) of low-lying excitations in one-dimensional disordered interacting systems are studied. The ground state EE shows a clear signature of localization, while low-lying excitations show a significantly longer localization length. The dependence of the localization as a function of interaction strength and sample length is studied using the density matrix renormalization group (DMRG). This behavior corresponds to the presence of the predicted many-particle critical energy in the vicinity of the ground state energy. The implications of these results on experiments are discussed.
The properties of the low-lying eigenvalues of the entanglement Hamiltonian and their relation to the localization length of a disordered interacting one-dimensional many-particle system are studied. The average of the first entanglement Hamiltonian level spacing is proportional to the ground-state localization length and shows the same dependence on the disorder and interaction strength as the localization length. This is the result of the fact that entanglement is limited to distances of order of the localization length. The distribution of the first entanglement level spacing shows a Gaussian-type behavior as expected for level spacings much larger than the disorder broadening. For weakly disordered systems (localization length larger than sample length), the distribution shows an additional peak at low-level spacings. This stems from rare regions in some samples which exhibit metalliclike behavior of large entanglement and large particle-number fluctuations. These intermediate microemulsion metallic regions embedded in the insulating phase are discussed.
Using exact diagonalization for non-interacting systems and density matrix renormalization group for interacting systems we show that Li and Haldane's conjecture on the correspondence between the low-lying many-particle excitation spectrum and the entanglement spectrum holds for disordered ballistic one-dimensional many-particle systems. In order to demonstrate the correspondence we develop a computationally efficient way to calculate the entanglement spectrum of low-lying excitation of non-interacting systems. We observe and explain the presence of an unexpected shell structure in the excitation spectrum. The low-lying shells are robust and survive even for strong electron-electron interactions.
Non-abelian symmetries are thought to be incompatible with many-body localization, but have been argued to produce in certain disordered systems a broad non-ergodic regime distinct from many-body localization. In this context, we present a numerical study of properties of highly-excited eigenstates of disordered chains with SU(3) symmetry. We find that while weakly disordered systems rapidly thermalize, strongly-disordered systems indeed exhibit non-thermal signatures over a large range of system sizes, similar to the one found in previously studied SU(2) systems. Our analysis is based on the spectral, entanglement, and thermalization properties of eigenstates obtained through large-scale exact diagonalization exploiting the full SU(3) symmetry.
We study the entanglement in momentum space of a disordered one-dimensional fermion lattice model with attractive interaction. We observe that the many-body localization transition can be characterized by behaviors of two components in entanglement spectrum. One of the components is related to paired-fermion entanglement which contributes to the long-range correlation in position space, and the vanishing of it indicates the emerged many-body localized phase. Based on this understanding, we identify the critical point between delocalized and localized phases for interaction of different strength. Additionally by method of entanglement spectrum, we provide a new evidence to show the transition of two phases induced by interaction, and find this phase transition is not influenced by the disorder. Our result shows key characteristics in entanglement for different phases in the system, and provides a novel perspective to understand many-body localization phenomenon.