Universal Anomaly of Dynamics at Phase Transition Points Induced by Pancharatnam-Berry Phase

TL;DR

This paper proposes that geometric phase effects, specifically the Pancharatnam-Berry phase, cause universal dynamical anomalies at phase transition points, affecting relaxation times and quantum coherence.

Contribution

It introduces the role of geometric phase effects in phase transition dynamics, linking them to anomalies and relaxation time divergence in quantum systems.

Findings

Geometric phase causes anomalies in relaxation times near phase transitions.

Quantum interference from geometric phase can prolong or shorten excited state relaxation.

Setting a phase shift of π can decouple states, leading to diverging relaxation times.

Abstract

Recently, dynamical anomalies more than critical slowing down are often observed near both the continuous and first-order phase transition points. We propose that the universal anomalies could originate from the geometric phase effects. A Pancharatnam-Berry phase is accumulated continuously in quantum states with the variation of tuning parameters. Phase transitions are supposed to induce a abrupt shift of the geometric phase. In our multi-level quantum model, the quantum interference induced by the geometric phase could prolong or shorten the relaxation times of excited states at phase transition points, which agrees with the experiments, models under sudden quenches and our semi-classical model. Furthermore, we find that by setting a phase shift of \text{\ensuremath{\pi}}, the excited state could be decoupled from the ground state by quantum cancellation so that the relaxation time even could diverge to infinity. Our work introduces the geometric phase to the study of conventional phase transitions and quantum phase transition, and could substantially extend the dephasing time of qubits for quantum computing.