Critical and strong-coupling phases in one- and two-bath spin-boson models

TL;DR

This paper introduces a high-accuracy variational matrix product state method to study phase transitions in dissipative quantum impurity models, revealing new phases and correcting previous results, and emphasizing the role of symmetries in quantum-to-classical correspondence.

Contribution

The authors develop a variational matrix product state approach with an optimized boson basis for accurate phase diagram analysis, and explore novel phases in XY-symmetric models with multiple baths.

Findings

Confirmed classical mean-field behavior for s<1/2 in sub-ohmic models

First results for XY-symmetric spin coupled to two baths, showing rich phase diagram

Identified the importance of symmetries in quantum-to-classical correspondence

Abstract

For phase transitions in dissipative quantum impurity models, the existence of a quantum-to-classical correspondence has been discussed extensively. We introduce a variational matrix product state approach involving an optimized boson basis, rendering possible high-accuracy numerical studies across the entire phase diagram. For the sub-ohmic spin-boson model with a power-law bath spectrum $\propto \w^s$, we confirm classical mean-field behavior for $s<1/2$, correcting earlier numerical renormalization-group results. We also provide the first results for an XY-symmetric model of a spin coupled to two competing bosonic baths, where we find a rich phase diagram, including both critical and strong-coupling phases for $s<1$, different from that of classical spin chains. This illustrates that symmetries are decisive for whether or not a quantum-to-classical correspondence exists.