Rabi Lattice models with discrete gauge symmetry: phase diagram and implementation in trapped ion quantum simulators

TL;DR

This paper explores a spin-boson chain with local Z2 symmetry, analyzing its phase diagram through various methods, and demonstrates its implementation in trapped ion quantum simulators to realize models with gauge invariance and phase transitions.

Contribution

It introduces a new spin-boson model with local gauge symmetry and details its phase diagram and potential for quantum simulation with trapped ions.

Findings

Existence of a first order phase transition in the model.

Validation of the phase diagram using multiple theoretical methods.

Feasibility of implementing the model in trapped ion systems.

Abstract

We study a spin-boson chain that exhibits a local Z2 symmetry. We investigate the quantum phase diagram of the model by means of perturbation theory, mean field theory and the Density Matrix Renormalization Group method. Our calculations show the existence of a first order phase transition in the region where the boson quantum dynamics is slow compared to the spin-spin interactions. Our model can be implemented with trapped ion quantum simulators, leading to a realization of minimal models showing local gauge invariance and first order phase transitions.