Defect production due to quenching through a multicritical point and along a gapless line

TL;DR

This paper reviews the dynamics of defect formation in a one-dimensional XY model during quantum quenches through critical points and gapless lines, highlighting modifications to Kibble-Zurek scaling in these scenarios.

Contribution

It introduces generalized scaling laws for defect density when quenching through multicritical points or along gapless lines, extending the Kibble-Zurek framework.

Findings

Defect density follows power-law decay with quenching rate.

Standard Kibble-Zurek scaling is modified near multicritical points.

Generalized scaling forms are proposed for complex critical scenarios.

Abstract

In this review, we study the quenching dynamics of a one-dimensional XY Hamiltonian in a transverse field under linear variation of different parameters of the Hamiltonian so that the system is driven through various critical points and gapless lines. It is observed that the density of defects falls off as a power law with the quenching rate $1/\tau$ where the power law is determined by the dimensionality of the underlying lattice and the critical exponents associated with the quantum critical point as predicted by Kibble-Zurek scaling. However, we show that when the system is driven through a multicritical point or along a gapless line, Kibble Zurek scaling needs to be modified. We discuss generalized scaling forms of the defect density for the above two situations.