Symmetry and Explicit Marking of the Critical Phase in Two-Bath Spin-Boson Model

TL;DR

This paper investigates the critical phase transition in a two-bath spin-boson model at zero temperature, overcoming computational challenges by symmetry-based optimization to accurately classify the phase transition.

Contribution

It introduces a symmetry-aware phonon basis optimization and an order parameter for the two-bath spin-boson model, enabling explicit determination of phase transition classification and criticality.

Findings

Identifies the critical phase with vanishing boson displacements in both baths.

Provides an accurate phase diagram with three model parameters.

Overcomes limitations of standard density matrix renormalization group methods.

Abstract

The spin-boson model is a paradigm for studying decoherence, relaxation, entanglement and other effects that arise in a quantum system coupled to environmental degrees of freedom. At zero temperature, a localization-delocalization phase transition is known to exist in the sub-Ohmic regime, where the standard density matrix renormalization group algorithm is inadequate due to the divergence in the number of low-frequency modes. This limitation is circumvented in this work by symmetrically optimizing the phonon basis and introducing an order parameter accounting for the U(1) symmetry for a two-bath spin-boson model, by which we are able to determine the classification and criticality of the phase transition explicitly. Compared with variational results, the critical phase is characterized by spontaneous vanishing of boson displacements in both the baths, resulting in an accurate phase diagram with three model parameters.