Quantum Phase Transition in the Sub-Ohmic Spin-Boson Model: Extended Coherent-state Approach

TL;DR

This paper introduces an extended coherent state method to accurately analyze quantum phase transitions in the sub-Ohmic spin-boson model, providing precise solutions and critical exponents for various bath spectral densities.

Contribution

The paper develops a novel extended coherent state approach applicable to qubit-boson systems, enabling accurate analysis of quantum phase transitions in the sub-Ohmic spin-boson model.

Findings

Accurately locates quantum phase transitions using fidelity measures.

Determines critical exponents for bath spectral density exponents s<1/2.

Provides a versatile method for systems with continuous spectral densities.

Abstract

We propose a general extended coherent state approach to the qubit (or fermion) and multi-mode boson coupling systems. The application to the spin-boson model with the discretization of a bosonic bath with arbitrary continuous spectral density is described in detail, and very accurate solutions can be obtained. The quantum phase transition in the nontrivial sub-Ohmic case can be located by the fidelity and the order-parameter critical exponents for the bath exponents $s<1/2$ can be correctly given by the fidelity susceptibility, demonstrating the strength of the approach.