The localization transition of the sub-Ohmic spin-boson model generates boson bath correlations that are, at low frequencies, analytically inaccessible to standard coherent-state-polaron variational ansatzes. In this paper, we introduce a ``squeezed polaron'' wavefunction incorporating generic Gaussian boson-boson correlations induced by the spin impurity. This gives the correct critical power-law scaling of bath observables near the localization transition together with a systematically improved ground state energy and a more accurate determination of the critical coupling. Our wavefunction captures the correct mean-field nature of the transition in the deep sub-Ohmic region. It also displays non-mean-field critical exponents in the shallow sub-Ohmic regime. Using the squeezed polaron as a starting point, we derive scattering phase shifts for bosons, and show how they encode the emergent energy scale that vanishes at the localization transition.The localization transition of the sub-Ohmic spin-boson model generates boson bath correlations that are, at low frequencies, analytically inaccessible to standard coherent-state-polaron variational ansatzes. In this paper, we introduce a ``squeezed polaron'' wavefunction incorporating generic Gaussian boson-boson correlations induced by the spin impurity. This gives the correct critical power-law scaling of bath observables near the localization transition together with a systematically improved ground state energy and a more accurate determination of the critical coupling. Our wavefunction captures the correct mean-field nature of the transition in the deep sub-Ohmic region. It also displays non-mean-field critical exponents in the shallow sub-Ohmic regime. Using the squeezed polaron as a starting point, we derive scattering phase shifts for bosons, and show how they encode the emergent energy scale that vanishes at the localization transition.

quant-pharXiv:2607.06850Jul 9, 20260 citations

Structure of spin polarons in the – – – model

Jan Bała

The European Physical Journal BJul 1, 20004 citations

Improved Silbey-Harris polaron ansatz for the spin-boson model

Shu He, Liwei Duan, Qing‐Hu Chen

In this paper, the well-known Silbey-Harris (SH) polaron ansatz for the spin-boson model is improved by adding orthogonal displaced Fock states. The obtained results for the ground state in all baths converge very quickly within finite displaced Fock states and corresponding SH results are corrected considerably. Especially for the sub-Ohmic spin-boson model, the converging results are obtained for $0<s<1/2$ in the fourth-order correction and very accurate critical coupling strengths of the quantum phase transition are achieved. Converging magnetization in the biased spin-boson model is also arrived at. Since the present improved SH ansatz can yield very accurate, even almost exact results, it should have wide applications and extensions in various spin-boson model and related fields.In this paper, the well-known Silbey-Harris (SH) polaron ansatz for the spin-boson model is improved by adding orthogonal displaced Fock states. The obtained results for the ground state in all baths converge very quickly within finite displaced Fock states and corresponding SH results are corrected considerably. Especially for the sub-Ohmic spin-boson model, the converging results are obtained for $0<s<1/2$ in the fourth-order correction and very accurate critical coupling strengths of the quantum phase transition are achieved. Converging magnetization in the biased spin-boson model is also arrived at. Since the present improved SH ansatz can yield very accurate, even almost exact results, it should have wide applications and extensions in various spin-boson model and related fields.

arXiv:1803.10142Physical review. B./Physical review. BMar 27, 201812 citations

Generalized Polaron Ansatz for the Ground State of the Sub-Ohmic Spin-Boson Model: An Analytic Theory of the Localization Transition

Alex W. Chin, Javier Prior, Susana F. Huelga +1 more

The sub-Ohmic spin-boson model possesses a quantum phase transition at zero temperature between a localized and a delocalized phase, whose properties have so far only been extracted by numerical approaches. Here we present an extension of the Silbey-Harris variational polaron ansatz which allows us to develop an analytical theory which correctly describes a continuous transition with mean-field exponents for 0<s<0.5. The critical properties, couplings, and observables we obtain show excellent agreement with existing numerical results, and we give an intuitive microscopic description of the changing correlations between the system and bath which suppress the spin coherence and drive the transition.The sub-Ohmic spin-boson model possesses a quantum phase transition at zero temperature between a localized and a delocalized phase, whose properties have so far only been extracted by numerical approaches. Here we present an extension of the Silbey-Harris variational polaron ansatz which allows us to develop an analytical theory which correctly describes a continuous transition with mean-field exponents for 0<s<0.5. The critical properties, couplings, and observables we obtain show excellent agreement with existing numerical results, and we give an intuitive microscopic description of the changing correlations between the system and bath which suppress the spin coherence and drive the transition.

arXiv:1102.1483Physical Review LettersOct 10, 2011123 citations

0<s<1/2

in the fourth-order correction and very accurate critical coupling strengths of the quantum phase transition are achieved. Converging magnetization in the biased spin-boson model is also arrived at. Since the present improved SH ansatz can yield very accurate, even almost exact results, it should have wide applications and extensions in various spin-boson model and related fields.