Quantum Phase Transition of Many Interacting Spins Coupled to a Bosonic Bath: static and dynamical properties

TL;DR

This paper investigates the equilibrium and dynamical properties of many interacting spins coupled to a bosonic bath, revealing a quantum phase transition in the Ohmic regime and analyzing relaxation behaviors using various computational methods.

Contribution

It demonstrates the occurrence of a Beretzinski-Thouless-Kosterlitz quantum phase transition in a spin-boson system and explores the effects of spin interactions and bath coupling on phase coherence and relaxation.

Findings

Quantum phase transition occurs in the Ohmic regime.

Critical coupling strength is independent of system size for nonzero spin interactions.

Relaxation exhibits non-monotonic temperature dependence, similar to the Kondo effect.

Abstract

By using worldline and diagrammatic quantum Monte Carlo techniques, matrix product state and a variational approach \`a la Feynman, we investigate the equilibrium properties and relaxation features of a quantum system of $N$ spins antiferromagnetically interacting with each other, with strength $J$, and coupled to a common bath of bosonic oscillators, with strength $\alpha$. We show that, in the Ohmic regime, a Beretzinski-Thouless-Kosterlitz quantum phase transition occurs. While for $J=0$ the critical value of $\alpha$ decreases asymptotically with $1/N$ by increasing $N$, for nonvanishing $J$ it turns out to be practically independent on $N$, allowing to identify a finite range of values of $\alpha$ where spin phase coherence is preserved also for large $N$. Then, by using matrix product state simulations, and the Mori formalism and the variational approach \`a la Feynman jointly, we unveil the features of the relaxation, that, in particular, exhibits a non monotonic dependence on the temperature reminiscent of the Kondo effect. For the observed quantum phase transition we also establish a criterion analogous to that of the metal-insulator transition in solids.