Boundary Perturbation Effects in Quantum Systems with Conserved Energy and Continuous Symmetry

TL;DR

This paper explores how boundary perturbations affect charge dynamics in one-dimensional quantum systems with energy conservation and continuous symmetry, revealing distinct phases and the conditions for their stability.

Contribution

It introduces a boundary-induced pumping mechanism and characterizes the conditions under which charge conservation is broken or preserved in both free and interacting models.

Findings

Two dynamical phases identified: charge fluctuation and charge conservation.

Frozen phase persists at high frequencies in Floquet systems, but not at low frequencies.

Effective energy conservation is crucial for the emergence of the frozen phase.

Abstract

We investigate one-dimensional systems with both energy conservation and a continuous symmetry, focusing on the impact of a boundary perturbation that breaks the continuous symmetry. Our study reveals two distinct dynamical phases: one in which the corresponding charge exhibits extensive fluctuations, and another where the charge remains conserved. These phases appear in both free and interacting models. We interpret this behavior through a boundary-induced pumping mechanism, which estimates the amplitude connecting two degenerate states from different charge sectors via a local charge-non-conserving operator. In the Floquet setting, we show that the frozen phase can survive at high driving frequencies but vanishes at low frequencies. This phenomenon is exact in free-fermion systems in the thermodynamic limit, but in interacting systems it appears only at finite system size. The emergence of the charge-frozen phase is attributed to effective energy conservation, and we demonstrate that this phase disappears when effective energy conservation is broken or replaced by other symmetries.