Thermodynamics of a Quantum Ising system coupled to a spin bath: Zero Temperature Results

TL;DR

This paper investigates the thermodynamic behavior of a quantum Ising system coupled to a spin bath at zero temperature, using a field theoretic approach to analyze phase transitions and response functions.

Contribution

It introduces a formalism that combines thermal and quantum fluctuations to study coupled spin systems, applying it to both a toy model and the real $LiHoF_4$ system.

Findings

Quantum Ising phase transition persists with spin bath coupling.

A hybridized mode of Ising and bath spins softens at the transition.

Long-range dipolar interactions influence the phase transition behavior.

Abstract

We study the effect of coupling a spin bath environment to a system which, at low energies, can be modeled as a quantum Ising system. A field theoretic formalism incorporating both thermal and quantum fluctuations is developed to derive results for the thermodynamic properties and response functions, both for a toy model and for the $LiHoF_4$ system, in which spin-8 electronic spins couple to a spin-$7/2$ nuclear spin bath: the phase transition then occurs in a system of electronuclear degrees of freedom, coupled by long-range dipolar interactions. The quantum Ising phase transition still exists, and one hybridized mode of the Ising and bath spins always goes soft at the transition.