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 in quantum spin glasses

Sudip Mukherjee, Sabyasachi Nag, Arti Garg

Jan 1, 20180 citations

The Behavior of Many-Body Localization of Quasi-Disordered Spin-1/2 Chains

Jiali Zhang, Taotao Hu, Hang Ren +5 more

International Journal of Theoretical PhysicsApr 27, 20220 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.