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

Journal of Physics Conference Series

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

Richard Berkovits

Published Mar 1, 2016• 2 citations
Publisher

Abstract

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.

DOI
10.1088/1742-6596/702/1/012005

Related papers

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

Richard Berkovits

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.

Annalen der Physik•Apr 27, 2017•5 citations

Characterizing the many-body localization transition using the entanglement spectrum

S D Geraedts, Nicolas Regnault, Rahul Nandkishore

We numerically explore the many body localization (MBL) transition through the lens of the entanglement spectrum . While a direct transition from localization to thermalization is believed to be obtained in the thermodynamic limit (the exact details of which remain an open problem), in finite system sizes there exists an intermediate 'quantum critical' regime. Previous numerical investigations have explored the crossover from thermalization to criticality, and have used this to place a numerical lower bound on the critical disorder strength for MBL. A careful analysis of the high energy part of the entanglement spectrum (which contains universal information about the critical point) allows us to study the crossover from criticality to MBL, and we find evidence for such a crossover which could allow us to place a numerical upper bound on the critical disorder strength for MBL.

arXiv:1705.00631•New Journal of Physics•Oct 16, 2017•47 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

Tracking the many-body localized to ergodic transition via extremal statistics of entanglement eigenvalues

Abhisek Samanta, Kedar Damle, Rajdeep Sensarma

Some interacting disordered many-body systems are unable to thermalize when the quenched disorder becomes larger than a threshold value. Although several properties of nonzero energy density eigenstates (in the middle of the many-body spectrum) exhibit a qualitative change across this many-body localization (MBL) transition, many of the commonly used diagnostics only do so over a broad transition regime. Here we provide evidence that the transition can be located precisely even at modest system sizes by sharply defined changes in the distribution of extremal eigenvalues of the reduced density matrix of subsystems. In particular, our results suggest that $p*={lim}_{{\ensuremath{\lambda}}_{2}\ensuremath{\rightarrow}ln{(2)}^{+}}{P}_{2}({\ensuremath{\lambda}}_{2})$, where ${P}_{2}({\ensuremath{\lambda}}_{2})$ is the probability distribution of the second lowest entanglement eigenvalue ${\ensuremath{\lambda}}_{2}$, behaves as an ``order parameter'' for the MBL phase: $p*>0$ in the MBL phase, while $p*=0$ in the ergodic phase with thermalization. Thus, in the MBL phase, there is a nonzero probability that a subsystem is entangled with the rest of the system only via the entanglement of one subsystem qubit with degrees of freedom outside the region. In contrast, this probability vanishes in the thermal phase.

arXiv:2001.10198•Physical review. B./Physical review. B•Sep 2, 2020•11 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

Many-Body-Localization Transition in the Strong Disorder Limit: Entanglement Entropy from the Statistics of Rare Extensive Resonances

Cécile Monthus

The space of one-dimensional disordered interacting quantum models displaying a many-body localization (MBL) transition seems sufficiently rich to produce critical points with level statistics interpolating continuously between the Poisson statistics of the localized phase and the Wigner–Dyson statistics of the delocalized phase. In this paper, we consider the strong disorder limit of the MBL transition, where the level statistics at the MBL critical point is close to the Poisson statistics. We analyze a one-dimensional quantum spin model, in order to determine the statistical properties of the rare extensive resonances that are needed to destabilize the MBL phase. At criticality, we find that the entanglement entropy can grow with an exponent 0 < α < 1 anywhere between the area law α = 0 and the volume law α = 1 , as a function of the resonances properties, while the entanglement spectrum follows the strong multifractality statistics. In the MBL phase near criticality, we obtain the simple value ν = 1 for the correlation length exponent. Independently of the strong disorder limit, we explain why, for the many-body localization transition concerning individual eigenstates, the correlation length exponent ν is not constrained by the usual Harris inequality ν ≥ 2 / d , so that there is no theoretical inconsistency with the best numerical measure ν = 0 . 8 ( 3 ) obtained by Luitz et al. (2015).

arXiv:1510.03711•Entropy•Apr 1, 2016•26 citations
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.
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.
We numerically explore the many body localization (MBL) transition through the lens of the entanglement spectrum . While a direct transition from localization to thermalization is believed to be obtained in the thermodynamic limit (the exact details of which remain an open problem), in finite system sizes there exists an intermediate 'quantum critical' regime. Previous numerical investigations have explored the crossover from thermalization to criticality, and have used this to place a numerical lower bound on the critical disorder strength for MBL. A careful analysis of the high energy part of the entanglement spectrum (which contains universal information about the critical point) allows us to study the crossover from criticality to MBL, and we find evidence for such a crossover which could allow us to place a numerical upper bound on the critical disorder strength for MBL.
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.
Some interacting disordered many-body systems are unable to thermalize when the quenched disorder becomes larger than a threshold value. Although several properties of nonzero energy density eigenstates (in the middle of the many-body spectrum) exhibit a qualitative change across this many-body localization (MBL) transition, many of the commonly used diagnostics only do so over a broad transition regime. Here we provide evidence that the transition can be located precisely even at modest system sizes by sharply defined changes in the distribution of extremal eigenvalues of the reduced density matrix of subsystems. In particular, our results suggest that $p*={lim}_{{\ensuremath{\lambda}}_{2}\ensuremath{\rightarrow}ln{(2)}^{+}}{P}_{2}({\ensuremath{\lambda}}_{2})$, where ${P}_{2}({\ensuremath{\lambda}}_{2})$ is the probability distribution of the second lowest entanglement eigenvalue ${\ensuremath{\lambda}}_{2}$, behaves as an ``order parameter'' for the MBL phase: p∗>0p*>0p∗>0 in the MBL phase, while p∗=0p*=0p∗=0 in the ergodic phase with thermalization. Thus, in the MBL phase, there is a nonzero probability that a subsystem is entangled with the rest of the system only via the entanglement of one subsystem qubit with degrees of freedom outside the region. In contrast, this probability vanishes in the thermal phase.
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 space of one-dimensional disordered interacting quantum models displaying a many-body localization (MBL) transition seems sufficiently rich to produce critical points with level statistics interpolating continuously between the Poisson statistics of the localized phase and the Wigner–Dyson statistics of the delocalized phase. In this paper, we consider the strong disorder limit of the MBL transition, where the level statistics at the MBL critical point is close to the Poisson statistics. We analyze a one-dimensional quantum spin model, in order to determine the statistical properties of the rare extensive resonances that are needed to destabilize the MBL phase. At criticality, we find that the entanglement entropy can grow with an exponent 0 < α < 1 anywhere between the area law α = 0 and the volume law α = 1 , as a function of the resonances properties, while the entanglement spectrum follows the strong multifractality statistics. In the MBL phase near criticality, we obtain the simple value ν = 1 for the correlation length exponent. Independently of the strong disorder limit, we explain why, for the many-body localization transition concerning individual eigenstates, the correlation length exponent ν is not constrained by the usual Harris inequality ν ≥ 2 / d , so that there is no theoretical inconsistency with the best numerical measure ν = 0 . 8 ( 3 ) obtained by Luitz et al. (2015).