Exposing local symmetries in distorted driven lattices via time-averaged invariants

TL;DR

This paper introduces time-averaged two-point currents as a tool to detect and analyze local symmetries in one-dimensional driven quantum lattices, even when global symmetry is broken.

Contribution

It derives spatially invariant two-point currents for time-periodic systems and demonstrates their use in identifying local symmetries and verifying wavefunction properties.

Findings

Two-point currents are invariant within local symmetry domains.

These currents can detect local symmetry deformations in static and driven lattices.

The method aids in symmetry-based convergence checks for broken global symmetries.

Abstract

Time-averaged two-point currents are derived and shown to be spatially invariant within domains of local translation or inversion symmetry for arbitrary time-periodic quantum systems in one dimension. These currents are shown to provide a valuable tool for detecting deformations of a spatial symmetry in static and driven lattices. In the static case the invariance of the two-point currents is related to the presence of time-reversal invariance and/or probability current conservation. The obtained insights into the wavefunctions are further exploited for a symmetry-based convergence check which is applicable for globally broken but locally retained potential symmetries.