Quantitative approach for the Dicke-Ising chain with an effective self-consistent matter Hamiltonian

TL;DR

This paper introduces a self-consistent effective matter Hamiltonian approach to analyze the Dicke-Ising chain, enabling precise phase diagram determination and improved accuracy in identifying phase transitions and phases.

Contribution

It develops a novel framework that maps the Dicke-Ising chain onto an effective Hamiltonian, allowing accurate numerical analysis without photon-spin quantum correlations.

Findings

Refined the location of the multicritical point with $10^{-4}$ accuracy.

Confirmed the existence of the antiferromagnetic superradiant phase in the thermodynamic limit.

Identified the antiferromagnetic superradiant phase as a many-body ground state of an effective transverse-field Ising model.

Abstract

In the thermodynamic limit, the Dicke-Ising chain maps exactly onto an effective self-consistent matter Hamiltonian with the photon field acting solely as a self-consistent effective field. As a consequence, no quantum correlations between photons and spins are needed to understand the quantum phase diagram. This enables us to determine the quantum phase diagram in the thermodynamic limit using numerical linked-cluster expansions combined with density matrix renormalization group calculations (NLCE+DMRG) to solve the resulting self-consistent matter Hamiltonian. This includes magnetically ordered phases with significantly improved accuracy compared to previous estimates. For ferromagnetic Ising couplings, we refine the location of the multicritical point governing the change in the order of the superradiant phase transition, reaching a relative accuracy of $10^{-4}$. For antiferromagnetic Ising couplings, we confirm the existence of the narrow antiferromagnetic superradiant phase in the thermodynamic limit. The effective matter Hamiltonian framework identifies the antiferromagnetic superradiant phase as the many-body ground state of an antiferromagnetic transverse-field Ising model with longitudinal field. This phase emerges through continuous Dicke-type polariton condensation from the antiferromagnetic normal phase, followed by a first-order transition to the paramagnetic superradiant phase. Thus, NLCE+DMRG provides a precise determination of the Dicke-Ising phase diagram in one dimension by solving the self-consistent effective matter Hamiltonian.