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

We study a fully connected quantum spin model resonantly coupled to a small environment of noninteracting 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.

Automated summary

We study the resonant coupling of a fully connected quantum spin model with a small environment of noninteracting spins and investigate the memory of initial state properties at long times. We find that certain properties of the initial state, in addition to total energy, can be remembered during the dynamics, even if they are not conserved. This memory effect occurs in a specific energy range, where an eigenstate quantum phase transition (ESQPT) takes place. The memory effect at that energy is robust to system-environment coupling until the coupling changes the energy of the ESQPT. This work reveals the independence of ESQPT memory on integrability and suggests that this mechanism may have a wider generality in preventing thermalization at ESQPTs.