Quantum criticality of the sub-Ohmic spin-boson model within displaced Fock states

TL;DR

This paper analytically investigates the quantum criticality of the sub-Ohmic spin-boson model using displaced Fock states, revealing new insights into critical exponents and the violation of quantum-classical mapping.

Contribution

It introduces a systematic, non-discretized analytical approach using displaced Fock states to study the spin-boson model's quantum critical behavior.

Findings

Magnetization critical exponent converges to 0.5 across the sub-Ohmic regime.

First evidence of violation of quantum-classical mapping for 1/2<s<1.

System always above its upper critical dimension in the sub-Ohmic bath.

Abstract

The spin-boson model is analytically studied using displaced Fock states (DFS) without discretization of the continuum bath. In the orthogonal displaced Fock basis, the ground-state wavefunction can be systematically improved in a controllable way. Interestingly, the zeroth-order DFS reproduces exactly the well known Silbey-Harris results. In the framework of the second-order DFS, the magnetization and the entanglement entropy are exactly calculated. It is found that the magnetic critical exponent $\beta$ is converged to $0.5$ in the whole sub-Ohmic bath regime $0<s<1$, compared with that by the exactly solvable generalized Silbey-Harris ansatz. It is strongly suggested that the system with sub-Ohmic bath is always above its upper critical dimension, in sharp contrast with the previous findings. This is the first evidence of the violation of the quantum-classical Mapping for $% 1/2<s<1$.