The Many-Body Localization Transition in a Generic One-Dimensional Quantum System

Abstract

We formulate a version of the strong disorder renormalization group (SDRG) to investigate the transition between the thermal phase and the many-body localized (MBL) phase in a generic closed, isolated, one-dimensional quantum system. In the thermal phase, the system relaxes to thermal equilibrium at nonzero temperature under its own dynamics. In the MBL phase, the many-body eigenstates are localized in the system's Hilbert space, transport is absent, and the system never relaxes to thermal equilibrium. The transition between these two phases is a novel quantum phase transition: it occurs at nonzero temperature and marks a transition between thermal many-body eigenstates with volume-law entanglement entropy and MBL eigenstates with area-law entanglement entropy. We obtain estimates for the correlation length critical exponent v ≈ 1:4 −􀀀 2:2. We also find that the entanglement entropy and its standard deviation are natural scaling variables and use them to obtain one of our estimates of v. Finally, we find that the spreading of entanglement and the transport of energy becomes increasingly slow as the system approaches the MBL transition from the thermal phase. This behavior indicates the existence of a thermal Griffiths regime in which rare, locally insulating regions dominate the long-time dynamics of the system.