Avoiding Ergodicity: Static and Dynamical Localization in Clean Interacting Systems

The many body localized phase provides the first and only example of a generic quantum interacting system that does not reach thermal equilibrium, and thereby violates the most fundamental principles of statistical physics. In the last decade, an enormous theoretical effort was invested in understanding the nature of this phase. It has attracted a similar deal of attention also within the experimental community, as it has the potential of storing information about initial states for long times and it allows the application of driving protocols without heating the system to an infinite temperature.

A key ingredient for achieving the MBL phase is randomness. The roots of this phase lie within the phenomenon of Anderson localization, where non-interacting particles form a localized non-ergodic phase. It is the question regarding the fate of Anderson localization in the presence of interactions that plants the seed for the discovery of the MBL phase.

We pose the question whether randomness is indeed an essential ingredient in achieving generic non-ergodic interacting phases. We propose the idea that the essential ingredient for MBL is localization, which does not necessarily mean disorder. We analyze the spectral and the dynamical properties of one-dimensional interacting fermions and spins in the presence of both disorder and linear potential. We show that by considering these two different localizing mechanisms, i.e., disorder and linear fields, one may construct a two-dimensional phase diagram which hosts a connected non-ergodic (MBL) phase.

We also examine the effect of periodic driving on the dynamics of many-body systems and show how such driving provides a general framework for controlling the transport properties in the system, as well establish mobile composite particles. We demonstrate that by including successive driving terms, it is possible to completely suppress the motion of particles, and effectively localize the many-body system, without the presence of disorder.

While at this point we can not make conclusive statements about the nature of this phase in higher dimensions, the lack of randomness and the low sensitivity to dimensionality may render these systems more accessible to a theoretical investigation in dimensions larger than one. Furthermore, we make steps towards employing well studied machine learning techniques to address the issue of finite size. Although we don’t show explicitly if it is possible to use such techniques to numerically solve larger system sizes, we show that a mapping of the disorder realization to the level statistics is easily learned.

1. Y. Baum, Evert P. L. van Nieuwenburg and Gil Refael, ”From Dynamical Localization to
Bunching in interacting Floquet Systems”, SciPost Phys. 5, 017 (2018).

2. Y. Baum, Evert P. L. van Nieuwenburg and Gil Refael, ”From Bloch Oscillations to Many
Body Localization in Clean Interacting Systems”, arXiv:1808.00471 (2018).