# Glassy Dynamics from Quark Confinement: Atomic Quantum Simulation of Gauge-Higgs Model on Lattice

## TL;DR

This paper explores atomic quantum simulations of the gauge-Higgs model using ultra-cold Bose gases, revealing phase diagrams, dynamical electric flux behavior, and potential glassy quantum dynamics relevant to many-body localization.

## Contribution

It extends previous work by analyzing the extended Bose-Hubbard model with nearest-neighbor interactions in 1D and 2D, uncovering glassy dynamics and phase structures from a gauge theory perspective.

## Key findings

- Identification of confinement, Coulomb, and Higgs phases in the model.
- Observation of slow, glassy quantum dynamics akin to experimental Rydberg atom chains.
- Implications for many-body localization in strongly-correlated quantum systems.

## Abstract

In the previous works, we proposed atomic quantum simulations of the U(1) gauge-Higgs model by ultra-cold Bose gases. By studying extended Bose-Hubbard models (EBHMs) including long-range repulsions, we clarified the locations of the confinement, Coulomb and Higgs phases. In this paper, we study the EBHM with nearest-neighbor repulsions in one and two dimensions at large fillings by the Gutzwiller variational method. We obtain phase diagrams and investigate dynamical behavior of electric flux from the gauge-theoretical point of view. We also study if the system exhibits glassy quantum dynamics in the absence and presence of quenched disorder. We explain that the obtained results have a natural interpretation in the gauge theory framework. Our results suggest important perspective on many-body localization in strongly-correlated systems. They are also closely related to anomalously slow dynamics observed by recent experiments performed on Rydberg atom chain, and our study indicates existence of similar phenomenon in two-dimensional space.