Quantum Monte Carlo Study of the Rabi-Hubbard Model

TL;DR

This study uses quantum Monte Carlo simulations to analyze the ground state phases of a one-dimensional Rabi-Hubbard model, revealing a phase diagram with coherent and incoherent phases and discussing the effects of counter-rotating terms.

Contribution

It provides the first detailed quantum Monte Carlo analysis of the Rabi-Hubbard model's phase diagram, highlighting the absence of Mott phases and conditions for model equivalence.

Findings

Two main phases: coherent and incoherent separated by a quantum phase transition.

Photon number diverges in the deep coherent phase, indicating instability.

Mott phases are absent due to counter-rotating terms.

Abstract

We study, using quantum Monte Carlo (QMC) simulations, the ground state properties of a one dimensional Rabi-Hubbard model. The model consists of a lattice of Rabi systems coupled by a photon hopping term between near neighbor sites. For large enough coupling between photons and atoms, the phase diagram generally consists of only two phases: a coherent phase and a compressible incoherent one separated by a quantum phase transition (QPT). We show that, as one goes deeper in the coherent phase, the system becomes unstable exhibiting a divergence of the number of photons. The Mott phases which are present in the Jaynes-Cummings-Hubbard model are not observed in these cases due to the presence of non-negligible counter-rotating terms. We show that these two models become equivalent only when the detuning is negative and large enough, or if the counter-rotating terms are small enough.