Dynamical Many-Body Localization in an Integrable Model

Takahiro Orito, Yoshihito Kuno, Ikuo Ichinose

We find that a flat-band fermion system with interactions and without disorders exhibits nonthermalized ergodicity-breaking dynamics, an analog of many-body localization (MBL). In the previous works we observed flat-band many-body localization (FMBL) in the Creutz ladder model. The origin of FMBL is a compact localized state governed by local integrals of motion (LIOMs), which are to be obtained explicitly. In this work we clarify the dynamical aspects of FMBL. We first study dynamics of two particles, and find that the states are not substantially modified by weak interactions, but the periodic time evolution of entanglement entropy emerges as a result of a specific mechanism inherent in the system. On the other hand, as the strength of the interactions is increased, the modification of the states takes place with inducing instability of the LIOMs. Furthermore, many-body dynamics of the system at finite fillings is numerically investigated by the time-evolving block decimation (TEBD) method. For a suitable choice of the filling, nonthermal and low entangled dynamics appears. This behavior is a typical example of the disorder-free FMBL.

Ang Yang, Zekai Chen, Yanliang Guo +3 more

V. I. Inozemtsev

Ben Craps, Oleg Evnin, Dmitry Kovrizhin +1 more

Conservation laws are of paramount importance in our understanding of classical and quantum dynamics. Here, we present a general framework for constructing exact quantum integrals of motion with the desired locality and quantum numbers, which will be illustrated for the case of many-body-localization (MBL). The latter has been understood theoretically in terms of the existence of an extensive number of local integrals of motion (LIOMs). Using our approach, we show that one can express the task of finding LIOMs as an optimization problem. For some specifications, this problem surprisingly connects to the question of finding classical ground states of spin-glass models. Our work unifies previous results obtained in the MBL context and reveals intriguing connections between many-body localization, spin-glass physics, and constrained optimization problems.

Bernard Faulend, Hrvoje Buljan, Antonio Štrkalj

Slow particle dynamics observed numerically even deep inside the many-body localized (MBL) regime has called the stability of MBL in the thermodynamic limit into question, and its microscopic origin remains unknown. Here, we show that this slow dynamics originates from many-body quantum beats that arise from the interaction-induced modulation of oscillations associated with single-particle hopping processes. We relate this mechanism to local integrals of motion (LIOMs) and show that it survives at arbitrarily large distances between LIOMs, is consistent with the stability of MBL in the thermodynamic limit, and is generic to many-body systems. We present new numerical results for quasiperiodic potentials and, based on the quantum beats mechanism, develop an analytical model that explains number entropy growth and quasiparticle spreading, as well as clarifies the distinct MBL phenomenology observed in quasiperiodic and random potentials. Lastly, we propose concrete signatures for observing many-body quantum beats in existing experimental platforms.

Léa Ferreira dos Santos, Jonathan Torres-Herrera