Quantum memory at an eigenstate phase transition in a weakly chaotic model

TL;DR

This paper investigates how a quantum spin model exhibits memory of initial states at an eigenstate quantum phase transition, demonstrating robustness of this memory effect against environmental coupling and its potential to prevent thermalization.

Contribution

It reveals that eigenstate quantum phase transitions can preserve initial state information in quantum systems, independent of integrability, broadening understanding of quantum memory mechanisms.

Findings

Memory of initial states persists at ESQPT energy levels.

Memory effect remains robust against weak system-environment coupling.

ESQPT can prevent thermalization in quantum systems.

Abstract

We study a fully connected quantum spin model resonantly coupled to a small environment of non-interacting spins, and investigate how initial state properties are remembered at long times. We find memory of initial state properties, in addition to the total energy, that are not conserved by the dynamics. This memory occurs in the middle of the spectrum where an eigenstate quantum phase transition (ESQPT) occurs as a function of energy. The memory effect at that energy in the spectrum is robust to system-environment coupling until the coupling changes the energy of the ESQPT. This work demonstrates the effect of ESQPT memory as independent of integrability and suggests a wider generality of this mechanism for preventing thermalization at ESQPTs.