Direct equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems: scaling of entanglement

TL;DR

This paper demonstrates a fundamental equivalence between quantum phase transitions in radiation-matter systems and magnetic systems, revealing universal scaling laws for entanglement and proposing an effective Hamiltonian.

Contribution

It establishes the universality class of the Dicke model's quantum phase transition and derives a universal finite-size scaling for entanglement.

Findings

Quantum phase transition in the Dicke model belongs to the same universality class as the transverse field XY model.

A universal finite-size scaling law for entanglement is derived.

An effective Hamiltonian for the qubit subsystem is proposed.

Abstract

We show that the quantum phase transition arising in a standard radiation-matter model (Dicke model) belongs to the same universality class as the infinitely-coordinated, transverse field XY model. The effective qubit-qubit exchange interaction is shown to be proportional to the square of the qubit-radiation coupling. A universal finite-size scaling is derived for the corresponding two-qubit entanglement (concurrence) and a size-consistent effective Hamiltonian is proposed for the qubit subsystem.