Universal dynamics across many-body localization phase transition

Benjamin Villalonga, Xiongjie Yu, David J. Luitz +1 more

Disorder and interactions can lead to the breakdown of statistical mechanics in quantum systems by transitioning to a many-body localized (MBL) phase. The thermal-to-MBL transition occurs by either increasing the amount of disorder present in a system or by decreasing its energy until it crosses the so-called mobility edge. The authors construct a set of approximate integrals of motion that are quasi-universal across the energy spectrum and, thus, across the mobility edge, too. Interestingly, MBL eigenstates under the mobility edge are aware of the existence of a thermal phase at a higher energy. The phase diagram is probed close to the transition and in the MBL phase. One finds a universal distribution of the strength of the couplings of the integrals of motion in the strong disorder limit.

Léa Ferreira dos Santos, Jonathan Torres-Herrera

Yevgeny Bar Lev, David R. Reichman

S. A. Parameswaran, Andrew C. Potter, Romain Vasseur

We review recent advances in understanding the universal scaling properties of non‐equilibrium phase transitions in non‐ergodic disordered systems. We discuss dynamical critical points (also known as eigenstate phase transitions) between different many‐body localized (MBL) phases, and between MBL and thermal phases. image

Artur Maksymov, Piotr Sierant, Jakub Zakrzewski

The level dynamics across the many-body localization transition is examined for XXZ spin model with a random magnetic field. We compare different scenarios of parameter-dependent motion in the system and consider measures such as level velocities, curvatures, as well as their fidelity susceptibilities. Studying the ergodic phase of the model we find that the level dynamics does not reveal the commonly believed universal behavior after rescaling the curvatures by the level velocity variance. At the same time, distributions of level curvatures and fidelity susceptibilities coincide with properly rescaled distributions for Gaussian orthogonal ensemble of random matrices. Profound differences exist depending on way the level dynamics is imposed in the many-body localized phase of the model in which the level dynamics can be understood with the help of local integrals of motion.

Matthew Rispoli, Alexander Lukin, Robert Schittko +5 more