Universal time evolution of string order parameter in quantum critical systems with boundary invertible or non-invertible symmetry breaking

TL;DR

This paper investigates how boundary symmetry-breaking affects the time evolution of string order parameters in quantum critical systems, revealing universal decay behaviors after quantum quenches and validating results through lattice models.

Contribution

It introduces a universal framework for understanding the time evolution of string order parameters under boundary symmetry-breaking in quantum critical systems, including both global and local quenches.

Findings

String order parameters decay exponentially after global quenches with boundary symmetry-breaking.

String order parameters decay as a power-law after local quenches with boundary symmetry-breaking.

Universal features in the time evolution are confirmed through lattice model simulations.

Abstract

The global symmetry, either invertible or non-invertible, has been extensively studied in two dimensional conformal field theories in recent years. When the theory is defined on a manifold with open boundaries, however, many interesting conformal boundary conditions will fully or partially break such global symmetry. In this work, we study the effect of symmetry-breaking boundaries or interfaces when the system is out of equilibrium. We show that the boundary or interface symmetry-breaking can be detected by the time evolution of string order parameters, which are constructed from the symmetry operators that implement the symmetry transformations. While the string order parameters are independent of time if the symmetry is preserved over the whole system, they evolve in time in a universal way if the boundary or interface breaks the symmetry. More explicitly, in the presence of boundary or interface symmetry-breaking, the string order parameters decay exponentially in time after a global quantum quench, and decay as a power-law in time after a local quantum quench. We also generalize our study to the case when the string order parameters are defined in a subsystem, which are related to the full counting statistics. It is found there are also universal features in the time evolution of string order parameters in this case. We verify our field theory results by studying the time evolution of these two different types of string order parameters in lattice models.