Geometric phase of quenched spin models

TL;DR

This paper investigates how the geometric phase of a spin in a quenched many-body system evolves over time, revealing phase-dependent behaviors and potential implications for entanglement thermalization.

Contribution

It analytically demonstrates the long-time behavior of the geometric phase depends on the post-quench phase and introduces a simplified open two-level system model for the spin dynamics.

Findings

Geometric phase exhibits periodic behavior in paramagnetic phases.

Differences in geometric phase behavior persist in finite systems.

Parity symmetry violations affect the geometric phase evolution.

Abstract

We consider a spin belonging to a many body system in a magnetically ordered phase, which initial state is a symmetry broken ground state. We assume that in this system a sudden quench of the Hamiltonian induces an evolution. We show that the long time behavior of the spin state, can be approximated by the one of an open two level system in which the evolution preserves all the symmetries of the Hamiltonian. Exploiting such a result we analyze the geometric phase associated with the evolution of the single spin state and we prove analytically that its long time behavior depends on the physical phase realized after the quench. When the system arrives in a paramagnetic phase, the geometric phase shows a periodic behavior that is absent in the case in which the system remains in the initial ordered phase. Such a difference also survives in finite size systems until boundary effects come into play. We also discuss the effects of a explicit violation of the parity symmetry of the Hamiltonian and possible applications to the problem of the entanglement thermalization.