Universal scaling in quenches across a discontinuity critical point

TL;DR

This paper investigates universal scaling laws for defect density and residual energy during slow parameter quenches near discontinuous quantum phase transitions, with numerical validation in a spin-1/2 XXZ chain.

Contribution

It derives universal scaling relations for quenches across a discontinuity critical point and explores their modifications at phase boundaries, confirmed through numerical analysis.

Findings

Universal scaling relations for defect density and residual energy.

Scaling of characteristic length scale during spatial quenches.

Numerical confirmation in spin-1/2 XXZ chain.

Abstract

We study slow variation (both spatial as well as temporal) of a parameter of a system in the vicinity of discontinuous quantum phase transitions, in particular, a discontinuity critical point (DCP) (or a first-order critical point). We obtain the universal scaling relations of the density of defects and the residual energy after a temporal quench, while we also unravel the scaling of the characteristic length scale associated with a spatial quench of a symmetry breaking field. Considering a spin-1/2 XXZ chain we establish how these scaling relations get modified when the DCP is located at the boundary of a gapless critical phase; these predictions are also confirmed numerically.