SU(2)-Symmetric Spin-Boson Model: Quantum Criticality, Fixed-Point Annihilation, and Duality

TL;DR

This paper uses high-accuracy quantum Monte Carlo simulations to study the SU(2)-symmetric spin-boson model, revealing fixed-point annihilation and a duality that explains the disappearance of the critical phase at a specific bath spectrum exponent.

Contribution

It provides the first non-perturbative numerical evidence for fixed-point collision and annihilation in the spin-boson model, and uncovers a duality symmetry that enables analytical predictions at strong coupling.

Findings

Fixed points collide and annihilate at s* = 0.6540(2).

Critical phase disappears for s < s*.

Duality symmetry relates fixed points and matches numerical results.

Abstract

The annihilation of two intermediate-coupling renormalization-group (RG) fixed points is of interest in diverse fields from statistical mechanics to high-energy physics, but has so far only been studied using perturbative techniques. Here we present high-accuracy quantum Monte Carlo results for the SU(2)-symmetric $S=1/2$ spin-boson (or Bose-Kondo) model. We study the model with a power-law bath spectrum $\propto \omega^s$ where, in addition to a critical phase predicted by perturbative RG, a stable strong-coupling phase is present. Using a detailed scaling analysis, we provide direct numerical evidence for the collision and annihilation of two RG fixed points at $s^\ast = 0.6540(2)$, causing the critical phase to disappear for $s<s^\ast$. In particular, we uncover a surprising duality between the two fixed points, corresponding to a reflection symmetry of the RG beta function, which we utilize to make analytical predictions at strong coupling which are in excellent agreement with numerics. Our work makes phenomena of fixed-point annihilation accessible to large-scale simulations, and we comment on the consequences for impurity moments in critical magnets.