The quantum phase transition in the sub-ohmic spin-boson model: Quantum Monte-Carlo study with a continuous imaginary time cluster algorithm

TL;DR

This paper introduces a continuous time cluster algorithm for the sub-ohmic spin-boson model, revealing classical critical exponents for s<1/2 and discussing discrepancies with renormalization group predictions.

Contribution

The paper presents a novel continuous time cluster algorithm for dissipative two-level systems and applies it to analyze the quantum phase transition in the sub-ohmic spin-boson model.

Findings

Critical exponents are classical for s<1/2.

Discrepancies with RG predictions are linked to dangerously irrelevant variables.

The algorithm effectively studies quantum phase transitions in dissipative systems.

Abstract

A continuous time cluster algorithm for two-level systems coupled to a dissipative bosonic bath is presented and applied to the sub-ohmic spin-Boson model. When the power s of the spectral function J(w) \propto w^s is smaller than 1/2, the critical exponents are found to be classical, mean-field like. Potential sources for the discrepancy with recent renormalization group predictions are traced back to the effect of a dangerously irrelevant variable.