Spectral response of disorder-free localized lattice gauge theories

TL;DR

This paper investigates the spectral response of disorder-free localized lattice gauge theories, revealing characteristic sharp peaks and zero-frequency response suppression, which can help distinguish this phase from paramagnetic states.

Contribution

It provides analytical and numerical analysis of spectral functions in disorder-free localized gauge theories, highlighting unique spectral features and their implications for experimental detection.

Findings

Spectral functions show sharp peaks and vanishing response at zero frequency.

Large clusters exhibit discrete peaks matching analytical estimates.

Information spreading halts due to real space fragmentation.

Abstract

We show that certain lattice gauge theories exhibiting disorder-free localization have a characteristic response in spatially averaged spectral functions: a few sharp peaks combined with vanishing response in the zero frequency limit. This reflects the discrete spectra of small clusters of kinetically active regions formed in such gauge theories when they fragment into spatially finite clusters in the localized phase due to the presence of static charges. We obtain the transverse component of the dynamic structure factor, which is probed by neutron scattering experiments, deep in this phase from a combination of analytical estimates and a numerical cluster expansion. We also show that local spectral functions of large finite clusters host discrete peaks whose positions agree with our analytical estimates. Further, information spreading, diagnosed by an unequal time commutator, halts due to real space fragmentation. Our results can be used to distinguish the disorder-free localized phase from conventional paramagnetic counterparts in those frustrated magnets which might realize such an emergent gauge theory.