The quantum phase transition and correlations in the multi-spin-boson model

TL;DR

This paper investigates quantum phase transitions in a multi-spin-boson model, revealing how a common bosonic bath induces ferromagnetic interactions, leading to collective freezing of two-level systems and mean-field critical behavior as the number of systems grows.

Contribution

It introduces a Monte Carlo simulation study of the multi-spin-boson model, analyzing the effects of a common bath and spatial separation on phase transition properties and correlations.

Findings

Critical coupling strength decreases as 1/N with increasing number of spins.

The phase transition belongs to the same universality class as the single spin-boson model for finite N.

Spatial separation affects the transition characteristics and inter-spin correlations.

Abstract

We consider multiple non-interacting quantum mechanical two-level systems coupled to a common bosonic bath and study its quantum phase transition with Monte Carlo simulations using a continuous imaginary time cluster algorithm. The common bath induces an effective ferromagnetic interaction between the otherwise independent two-level systems, which can be quantified by an effective interaction strength. For degenerate energy levels above a critical value of the bath coupling strength $\alpha$ all two-level systems freeze into the same state and the critical value $\alpha_c$ decreases asymptotically as $1/N$ with increasing $N$. For a finite number, $N$, of two-level systems the quantum phase transition (at zero temperature) is in the same universality class as the single spin-boson model, in the limit $N\to\infty$ the system shows mean-field critical behavior independent of the power of the spectral function of the bosonic bath. We also study the influence of a spatial separation of the spins in a bath of bosonic modes with linear dispersion relation on the location and characteristics of the phase transition as well as on correlations between the two-level systems.