Many-body localization

Anonymous

Shankar Balasubramanian, Yunxiang Liao, Victor M. Galitski

Recently, a structure called the localization landscape was shown to accurately predict the location of eigenfunctions in the single-particle Anderson model. Here, the authors generalize the localization landscape to a large class of interacting many-body systems. They use the many-body localization landscape (MBLL) to prove decay estimates of eigenstates, and show robustness of the MBLL to weak interactions and hopping by deriving a convergent locator expansion. This establishes the MBLL as a method for efficiently estimating low-energy eigenstates and understanding possible phases in MBL models.

Anushya Chandran, Philip J. D. Crowley

as many-body localization.

Maksym Serbyn, Zlatko Papić, Dmitry A. Abanin

We construct a complete set of local integrals of motion that characterize the many-body localized (MBL) phase. Our approach relies on the assumption that local perturbations act locally on the eigenstates in the MBL phase, which is supported by numerical simulations of the random-field XXZ spin chain. We describe the structure of the eigenstates in the MBL phase and discuss the implications of local conservation laws for its nonequilibrium quantum dynamics. We argue that the many-body localization can be used to protect coherence in the system by suppressing relaxation between eigenstates with different local integrals of motion.

C. P. Burgess

Peter Prelovšek, O. S. Barišić, Marcin Mierzejewski

Within the standard model of many-body localization, i.e., the disordered chain of spinless fermions, we investigate how the interaction affects the many-body states in the basis of noninteracting localized Anderson states. From this starting point we follow the approach that uses a reduced basis of many-body states. Together with an extrapolation to the full basis, it proves to be efficient for the evaluation of the stiffnesses of local observables, which remain finite within the nonergodic regime and represent the hallmark of the many-body localization (MBL). The method enables a larger span of system sizes and, within the MBL regime, allows for a more careful analysis of the size scaling of calculated quantities. On the other hand, the survival stiffness as the representative of nonlocal quantities, reveals limitations of the reduced-basis approach.