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arXiv:1202.5719

Parity breaking and scaling behavior in the spin-boson model

Tao Liu, Mang Feng, Li, Lei, Yang, Wanli, K. Wang

Published Feb 26, 2012• 0 citations
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Abstract

We study the breaking of parity in the spin-boson model and demonstrate unique scaling behavior of the magnetization and entanglement around the critical points for the parity breaking after suppressing the infrared divergence existing inherently in the spectral functions for Ohmic and sub-Ohmic dissipations. Our treatment is basically analytical and of generality for all types of the bath. We argue that the conventionally employed spectral function is not fully reasonable and the previous justification of quantum phase transition for localization needs to be more seriously reexamined.

DOI
10.48550/arxiv.1202.5719

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We study the breaking of parity in the spin-boson model and demonstrate unique scaling behavior of the magnetization and entanglement around the critical points for the parity breaking after suppressing the infrared divergence existing inherently in the spectral functions for Ohmic and sub-Ohmic dissipations. Our treatment is basically analytical and of generality for all types of the bath. We argue that the conventionally employed spectral function is not fully reasonable and the previous justification of quantum phase transition for localization needs to be more seriously reexamined.
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A generalized trial wave function termed as the ``multi-D1{D}_{1}D1​ ansatz'' has been developed to study the ground state of the spin-boson model with simultaneous diagonal and off-diagonal coupling in the sub-Ohmic regime. Ground-state properties including energy and spin polarization are investigated, and the results are consistent with those from exact diagonalization and density matrix renormalization group approaches for the cases involving two oscillators and two baths described by a continuous spectral density function. Breakdown of the rotational and parity symmetries along the continuous quantum phase transition separating the localized phase from the critical phase has been uncovered. Moreover, the phase boundary is determined accurately with the corresponding rotational- and parity-symmetry parameters. A critical value of the spectral exponent s∗=0.49(1){s}^{*}=0.49(1)s∗=0.49(1) is predicted in the weak coupling limit, which is in agreement with the mean-field prediction of 1/21/21/2, but much smaller than the earlier literature estimate of 0.75(1)0.75(1)0.75(1).
An analytic ground state is proposed for the unbiased spin-boson Hamiltonian, which is non-Gaussian and beyond the Silbey-Harris ground state with lower ground state energy. The infrared catastrophe in Ohmic and sub-Ohmic bosonic bath plays an important role in determining the degeneracy of the ground state. We show that the infrared divergence associated with the displacement of the nonadiabatic modes in bath may be removed from the proposed ground state for the coupling α < αc. Then αc is the quantum critical point of a transition from non-degenerate to degenerate ground state and our calculated αc agrees with previous numerical results.
We propose a general extended coherent state approach to the qubit (or fermion) and multimode 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<1/2s<1/2s<1/2 can be correctly given by the fidelity susceptibility, demonstrating the strength of the approach.
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.