Critical and Strong-Coupling Phases in One- and Two-Bath Spin-Boson Models

Abstract

For phase transitions in dissipative quantum impurity models, the existence of a quantum-toclassical 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 ∝ ω 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.

Quantum criticality of the sub-Ohmic spin-boson model

“…18 argued that the NRG results for δ and β are invalid for a reason that is entirely separate from mass-flow error, namely the NRG truncation of the bosonic Hilbert space. (A variational procedure has recently been proposed 23,24 to circumvent the effects of bosonic truncation.) However, it appears unnatural that two independent sources of errors should conspire to yield results that are consistent with hyperscaling.…”

Quantum critical point of spin-boson model and infrared catastrophe in bosonic bath

“…In last ten years, various numerical techniques were used for calculation of the QCP in the SBM, such as the numerical renormalization group (NRG) [3,4,5], the quantum Monte Carlo (QMC) [8], the method of sparse polynomial space representation [9], the extended coherent state approach [10], and the variational matrix product state approach [11]. Besides, recently an extension of the Silbey-Harris ground state was proposed by Zhao et al [12] and Chin et al [13] to study the QPT in the s = 1/2 sub-Ohmic SBM.…”

Communication: Spin-boson model with diagonal and off-diagonal coupling to two independent baths: Ground-state phase transition in the deep sub-Ohmic regime

“…Stated differently, a special type of quantum phase transitions is identified, which is confirmed by results of the density matrix renormalization group (DMRG) calculations, a method that has been proven to be robust in numerous studies of quantum phase transitions in the usual SBM. 14 Previous studies, such as DMRG, numerical renormalization group, and quantum Monte Carlo, have revealed that in the absence of bias σ z will be zero if α is below some critical value α c ( ), placing the system in a delocalized phase. If α > α c , σ z acquires a finite value and the system enters a localized phase.…”

“…(6), competition between the baths poses a significant challenge to the numerical simulations due to an increased total boson number that must be kept. DMRG calculations 14 have so far revealed that if s =s < 1/2 and σ x and σ z coupled to two boson baths with equivalent coupling strengths (α = β), the spin is situated in a localized state. Furthermore, to obtain a deeper insight into the properties of the two-bath SBM, it is interesting to investigate the deep sub-Ohmic regime of the two-bath SBM with differing α and β, for a general scenario of s =s and s =s.…”