Abstract We study the many-body localization (MBL) properties of the Heisenberg XXZ spin- $\frac 12$ chain in a random magnetic field. We prove that the system exhibits localization in any given energy interval at the bottom of the spectrum in a nontrivial region of the parameter space. This region, which includes weak interaction and strong disorder regimes, is independent of the size of the system and depends only on the energy interval. Our approach is based on the reformulation of the localization problem as an expression of quasi-locality for functions of the random many-body XXZ Hamiltonian. This allows us to extend the fractional moment method for proving localization, previously derived in a single-particle localization context, to the many-body setting.Abstract We study the many-body localization (MBL) properties of the Heisenberg XXZ spin- $\frac 12$ chain in a random magnetic field. We prove that the system exhibits localization in any given energy interval at the bottom of the spectrum in a nontrivial region of the parameter space. This region, which includes weak interaction and strong disorder regimes, is independent of the size of the system and depends only on the energy interval. Our approach is based on the reformulation of the localization problem as an expression of quasi-locality for functions of the random many-body XXZ Hamiltonian. This allows us to extend the fractional moment method for proving localization, previously derived in a single-particle localization context, to the many-body setting.

arXiv:2210.14873Forum of Mathematics SigmaJan 1, 20245 citations

Many-body localization for the random XXZ spin chain in fixed energy intervals

Alexander Elgart, Abel Klein

It is shown that the infinite random Heisenberg XXZ spin- $\frac12$ chain exhibits slow propagation of information (logarithmic light cone), a key signature of many-body localization (MBL), in any fixed energy interval at the bottom of the spectrum. The relevant parameter regime, which covers both weak interaction and strong disorder, is determined solely by the energy interval.It is shown that the infinite random Heisenberg XXZ spin-$\frac12$ chain exhibits slow propagation of information (logarithmic light cone), a key signature of many-body localization (MBL), in any fixed energy interval at the bottom of the spectrum. The relevant parameter regime, which covers both weak interaction and strong disorder, is determined solely by the energy interval.

arXiv:2602.01441Feb 1, 20260 citations

On Many-Body Localization for Quantum Spin Chains

John Z Imbrie

arXiv:1403.7837Journal of Statistical PhysicsApr 1, 2016652 citations

Many-body localization in the quantum random energy model

Chris R. Laumann, Arijeet Pal

Bulletin of the American Physical SocietyMar 3, 20140 citations

Droplet localization in the random XXZ model and its manifestations

Alexander Elgart, A Klein, Günter Stolz

Abstract We examine many-body localization properties for the eigenstates that lie in the droplet sector of the random-field spin- 1 2 XXZ chain. These states satisfy a basic single cluster localization property (SCLP), derived in Elgart et al (2018 J. Funct. Anal . (in press)). This leads to many consequences, including dynamical exponential clustering, non-spreading of information under the time evolution, and a zero velocity Lieb–Robinson bound. Since SCLP is only applicable to the droplet sector, our definitions and proofs do not rely on knowledge of the spectral and dynamical characteristics of the model outside this regime. Rather, to allow for a possible mobility transition, we adapt the notion of restricting the Hamiltonian to an energy window from the single particle setting to the many body context.Abstract We examine many-body localization properties for the eigenstates that lie in the droplet sector of the random-field spin- 1 2 XXZ chain. These states satisfy a basic single cluster localization property (SCLP), derived in Elgart et al (2018 J. Funct. Anal . (in press)). This leads to many consequences, including dynamical exponential clustering, non-spreading of information under the time evolution, and a zero velocity Lieb–Robinson bound. Since SCLP is only applicable to the droplet sector, our definitions and proofs do not rely on knowledge of the spectral and dynamical characteristics of the model outside this regime. Rather, to allow for a possible mobility transition, we adapt the notion of restricting the Hamiltonian to an energy window from the single particle setting to the many body context.

arXiv:1707.09665Journal of Physics A Mathematical and TheoreticalOct 31, 20175 citations

Abstract We study the many-body localization (MBL) properties of the Heisenberg XXZ spin-

\frac 12

chain in a random magnetic field. We prove that the system exhibits localization in any given energy interval at the bottom of the spectrum in a nontrivial region of the parameter space. This region, which includes weak interaction and strong disorder regimes, is independent of the size of the system and depends only on the energy interval. Our approach is based on the reformulation of the localization problem as an expression of quasi-locality for functions of the random many-body XXZ Hamiltonian. This allows us to extend the fractional moment method for proving localization, previously derived in a single-particle localization context, to the many-body setting.

It is shown that the infinite random Heisenberg XXZ spin-

\frac12

chain exhibits slow propagation of information (logarithmic light cone), a key signature of many-body localization (MBL), in any fixed energy interval at the bottom of the spectrum. The relevant parameter regime, which covers both weak interaction and strong disorder, is determined solely by the energy interval.