Non-thermalized Dynamics of Flat-Band Many-Body Localization

TL;DR

This paper demonstrates that flat-band fermion systems with interactions, but no disorder, can exhibit non-thermalized, ergodicity-breaking dynamics similar to many-body localization, with explicit LIOMs and low entanglement at finite fillings.

Contribution

It clarifies the dynamical mechanisms of flat-band many-body localization and explicitly constructs local integrals of motion in a disorder-free system.

Findings

Weak interactions do not significantly alter two-particle states.

Periodic entanglement entropy evolution emerges due to system-specific mechanisms.

Finite filling systems show non-thermal, low-entanglement dynamics characteristic of FMBL.

Abstract

We find that a flat-band fermion system with interactions and without disorders exhibits non-thermalized 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 time-evolving block decimation (TEBD) method. For a suitable choice of the filling, non-thermal and low entangled dynamics appears. This behavior is a typical example of the disorder-free FMBL.