Thermalization at the Many-body localization Phase Transition

Oles Shtanko, Iman Marvian, Seth Lloyd

Kartiek Agarwal, Ehud Altman, Eugene Demler +3 more

The low‐frequency response of systems near the many‐body localization phase transition, on either side of the transition, is dominated by contributions from rare regions that are locally “in the other phase”, i.e., rare localized regions in a system that is typically thermal, or rare thermal regions in a system that is typically localized. Rare localized regions affect the properties of the thermal phase, especially in one dimension, by acting as bottlenecks for transport and the growth of entanglement, whereas rare thermal regions in the localized phase act as local “baths” and dominate the low‐frequency response of the MBL phase. We review recent progress in understanding these rare‐region effects, and discuss some of the open questions associated with them: in particular, whether and in what circumstances a single rare thermal region can destabilize the many‐body localized phase. image

Ehud Altman

Vedika Khemani, S. P. Lim, D. N. Sheng +1 more

Some quantum systems can enter a many-body localized (MBL) phase, where the particles do not settle into thermal equilibrium but remain stuck in some initial state. A new theoretical analysis explores the transition between MBL and thermal phases and finds that the transition is driven by the growth of a network of quantum entanglement.

Jagannath Sutradhar, Soumi Ghosh, Sthitadhi Roy +3 more

We implement a recursive Green's function method to extract the Fock space (FS) propagator and associated self-energy across the many-body localization (MBL) transition, for one-dimensional interacting fermions in a random on-site potential. We show that the typical value of the imaginary part of the local FS self-energy, ${\mathrm{\ensuremath{\Delta}}}_{t}$, related to the decay rate of an initially localized state, acts as a probabilistic order parameter for the thermal to MBL phase transition and can be used to characterize critical properties of the transition as well as the multifractal nature of MBL states as a function of disorder strength $W$. In particular, we show that a fractal dimension ${D}_{s}$ extracted from ${\mathrm{\ensuremath{\Delta}}}_{t}$ jumps discontinuously across the transition, from ${D}_{s}<1$ in the MBL phase to ${D}_{s}=1$ in the thermal phase. Moreover, ${\mathrm{\ensuremath{\Delta}}}_{t}$ follows an asymmetrical finite-size scaling form across the thermal-MBL transition, where a nonergodic volume in the thermal phase diverges with a Kosterlitz-Thouless--like essential singularity at the critical point ${W}_{c}$ and controls the continuous vanishing of ${\mathrm{\ensuremath{\Delta}}}_{t}$ as ${W}_{c}$ is approached. In contrast, a correlation length ($\ensuremath{\xi}$) extracted from ${\mathrm{\ensuremath{\Delta}}}_{t}$ exhibits a power-law divergence on approaching ${W}_{c}$ from the MBL phase.

Adam M. Kaufman, Eric Tai, Alex Lukin +5 more