The geometric phase and the dynamics of quantum phase transition induced by a linear quench

TL;DR

This paper explores how the geometric phase influences the dynamics of quantum phase transitions in the transverse Ising model during a linear quench, linking spin fluctuations to quasiparticle excitations and defect formation.

Contribution

It introduces a novel analysis of the geometric phase's role in quantum phase transition dynamics under a linear quench in the transverse Ising model.

Findings

Kink density scales as τ_q^{-1/2} during the transition.

Spin-spin correlation at criticality is estimated.

Random geometric phase fluctuations relate to quasiparticle excitation probability.

Abstract

We have analysed here the role of the geometric phase in dynamical mechanism of quantum phase transition in the transverse Ising model. We have investigated the system when it is driven at a fixed rate characterized by a quench time $\tau_q$ across the critical point from a paramagnetic to ferromagnetic phase. Our argument is based on the fact that the spin fluctuation occurring during the critical slowing down causes random fluctuation in the ground state geometric phase at the critical regime. The correlation function of the random geometric phase determines the excitation probability of the quasiparticles, which are excited during the transition from the inital paramagnetic to the ferromagnetic phase. This helps us to evaluate the number density of the kinks formed during the transition, which is found to scale as $\tau_q^{-\frac{1}{2}}$. In addition, we have also estimated the spin-spin correlation at criticality.