Quantum phase transition in a quantum Rabi square with next-nearest-neighbor hopping

TL;DR

This paper introduces a quantum Rabi square model with next-nearest-neighbor hopping, revealing phase transitions and artificial gauge effects, advancing quantum simulation and materials research.

Contribution

It demonstrates how next-nearest-neighbor hopping induces phase transitions and mimics gauge phases, providing a new approach for quantum control and modeling frustrated quantum systems.

Findings

First-order phase transition between antiferromagnetic and frustrated superradiant phases.

Second-order phase transition between normal and superradiant phases.

Next-nearest hopping acts as an artificial gauge phase.

Abstract

We propose a quantum Rabi square model where both the nearest-neighbor and the next-nearest-neighbor photon hopping are allowed among four quantum Rabi systems located at the vertices of a square. By tuning the next-nearest hopping strength, we realize a first-order phase transition between the antiferromagnetic superradiant phase and the frustrated superradiant phase, as well as a second-order phase transition between the normal and the superradiant phases. To understand the emergence of such phases, we show analytically that the effect induced by next-nearest hopping is equivalent to that of an artificial gauge phase. Our findings suggest that the next-nearest-neighbor hopping can serve as an alternative for the gauge phase to realize quantum control in applications of quantum simulation and quantum materials, and that our model represents a basic building block for the frustrated $J_1$-$J_2$ quantum spin model on square lattices.