Quantum phase transition in the one-dimensional Dicke-Hubbard model with coupled qubits

TL;DR

This paper investigates the ground state phase diagram of a one-dimensional two-qubit Dicke-Hubbard model with XY interactions, revealing rich quantum phase transitions, triple points, and the impact of counter-rotating wave terms.

Contribution

It introduces a combined numerical approach using cluster mean-field theory and matrix product states to analyze the model's ground state, including effects of counter-rotating terms.

Findings

Identifies a phase transition between Mott-insulating and superfluid phases.

Discovers two quantum triple points with coexistence of three phases.

Shows counter-rotating terms significantly affect non-local correlations.

Abstract

We study the ground state phase diagram of a one-dimensional two qubits Dicke-Hubbard model with XY qubit-qubit interaction. We use a numerical method combing the cluster mean-field theory and the matrix product state(MPS) to obtain the exact wave function of the ground state. When counter-rotating wave terms(CRTs) in the qubit-cavity coupling are neglected, we observe a rich phase diagram including a quantum phase transition between the Mott-insulating phase and the superfluid phase. This phase transition can be either the first-order or the second-order type depending on whether the total angular momentum changes across the phase diagram. Moreover, we observe two quantum triple points, at which three different phases coexist, with both positive and negative XY interactions. By further considering the effect of CRTs, we find that the main feature in the previous phase diagram, including the existence of quantum triple points, is retained. We also show that CRTs extremely demolish the non-local correlations in the coherent phase.