On the finite size behavior of quantum collective spin systems

TL;DR

This paper analyzes the finite size effects in the adiabatic Dicke model, linking it to the uniaxial collective spin model, and provides a detailed characterization of observable scaling near the quantum phase transition.

Contribution

It introduces an approximate continuum approach to study the finite size behavior of the Dicke model and relates its properties to the uniaxial spin model for the first time.

Findings

Characterization of the uniaxial spin model using continuum approximation

Evaluation of observable scaling near the quantum phase transition

Insights into finite size effects in collective spin systems

Abstract

We discuss the finite size behavior of the adiabatic Dicke model, describing the collective coupling of a set of N-two level atoms (qubits) to a faster (electromagnetic) oscillator mode. The energy eigen-states of this system are shown to be directly related to those of another widely studied collective spin model, the uniaxial one. By employing an approximate continuum approach, we obtain a complete characterization of the properties of the latter, which we then use to evaluate the scaling properties of various observables for the original Dicke model near its quantum phase transition.