Finite-size subthermal regime in disordered SU(N)-symmetric Heisenberg chains

TL;DR

This paper investigates the persistence of subthermal, non-ergodic behavior in disordered SU(N)-symmetric Heisenberg chains, extending previous SU(2) studies to larger systems and different symmetries, revealing robustness at intermediate times.

Contribution

It extends the analysis of subthermal regimes to larger SU(N) systems using tDMRG, demonstrating the persistence of non-ergodic behavior across different symmetries and system sizes.

Findings

Subthermal behavior persists at intermediate times and stronger disorder.

Thermalization tendencies increase with system size but subthermal regimes remain observable.

SU(3) systems show broader thermal phases compared to SU(2).

Abstract

SU(N) symmetry is incompatible with the many-body localized (MBL) phase, even when strong disorder is present. However, recent studies have shown that finite-size SU(2) systems exhibit non-ergodic, subthermal behavior, characterized by the breakdown of the eigenstate thermalization hypothesis, and by the excited eigenstates entanglement entropy that is intermediate between area and volume law. In this work, we extend previous studies of the SU(2)-symmetric disordered Heisenberg model to larger systems, using the time-dependent density matrix renormalization group (tDMRG) method. We simulate quench dynamics from weakly entangled initial states up to long times, finding robust subthermal behavior at stronger disorder. Although we find an increased tendency towards thermalization at larger system sizes, the subthermal regime persists at intermediate time scales, nevertheless, and therefore should be accessible experimentally. At weaker disorder, we observe signatures of thermalization, however, entanglement entropy exhibits slow sublinear growth, in contrast to conventional thermalizing systems. Furthermore, we study dynamics of the SU(3)-symmetric disordered Heisenberg model. Similarly, strong disorder drives the system into subthermal regime, albeit thermalizing phase is broader compared to the SU(2) case. Our findings demonstrate the robustness of the subthermal regime in spin chains with non-Abelian continuous symmetry, and are consistent with eventual thermalization at large system sizes and long time scales, suggested by previous works.