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

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 proportional to cos 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* = 0.6540(2), causing the critical phase to disappear for s < s*. 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.

Automated summary

This study presents high-accuracy quantum Monte Carlo results for the annihilation of two intermediate-coupling renormalization-group (RG) fixed points in the SU(2)-symmetric S = 1/2 spin-boson model. The collision and annihilation of the RG fixed points at s* = 0.6540(2) are revealed through detailed scaling analysis, providing direct numerical evidence for the disappearance of the critical phase.