One-dimensional $Z_2$ lattice gauge theory in periodic Gauss-law sectors

TL;DR

This paper investigates a one-dimensional $Z_2$ lattice gauge theory across various Gauss law sectors, revealing rich phases like confined, deconfined, and supersolid states through DMRG calculations.

Contribution

It demonstrates how different Gauss law sectors can be accessed via initial conditions in quantum simulators and characterizes their ground state properties.

Findings

Identification of confined and deconfined phases

Observation of charge density waves and supersolids

Analysis of phase transitions as a function of matter density

Abstract

We calculate the properties of a one-dimensional $Z_2$ lattice gauge theory in different Gauss law sectors, corresponding to different configurations of static charges set by the orientations of the gauge spins. Importantly, in quantum simulator experiments these sectors can be accessed without adding any additional physical particles or changing the Hamiltonian: The Gauss law sectors are simply set by the initial conditions. We study the interplay between conservation laws and interactions when the static charges are chosen to form periodic patterns. We classify the different Gauss law sectors and use the density matrix renormalization group to calculate the ground state compressibility, density profiles, charge density wave order parameters, and single particle correlation functions as a function of matter density. We find confined and deconfined phases, charge density waves, correlated insulators, and supersolids.