Quantum phase transitions of the anisotropic Dicke-Ising model in driven Rydberg arrays

TL;DR

This paper investigates phase transitions in a tunable Rydberg atom array modeled by a generalized Dicke-Ising Hamiltonian, revealing complex critical phenomena and the nature of various phase transitions through advanced quantum Monte Carlo simulations.

Contribution

It introduces an improved quantum Monte Carlo method for analyzing the model and characterizes the order of phase transitions and effects of quantum fluctuations.

Findings

Identification of superradiant and solid phases in the model

Determination of second-order and first-order phase transitions

Observation of quantum fluctuation effects on phase stability

Abstract

We study the properties of a generalized Dicke-Ising model realized with an array of Rydberg atoms, driven by microwave electric fields and coupled to an optical cavity. As this platform allows for a precisely tunable anisotropy parameter, the model exhibits a rich landscape of phase transitions and critical phenomena, induced by the interplay of rotating-wave, counter-rotating-wave, and Ising interactions. We develop an improved quantum Monte Carlo algorithm based on the stochastic series expansion that explicitly tracks the Fock state of the quantum cavity. In the superradiant (SR) phase, this allows us to determine, through data collapse, the scaling laws of the photon number. We also demonstrate the vanishing of parity symmetry in finite-size simulations and show that the Rydberg blockade leads to a significant suppression of cavity occupation. Notably, stronger quantum fluctuations induced by the counter-rotating wave terms slightly favor the superradiant solid (SRS) phase over the Solid-1/2 state. Finally, we confirm that the SR phase transition and the transition from the Solid-1/2 to the SRS are second-order. In contrast, the transitions from the Solid-1/2 or SRS to the SR phase are both first-order for any value of the normalized anisotropy parameter.