We present energy and free-energy analyses on all variational schemes used so far in the spin-boson model at both $T=0$ and $T\ensuremath{\ne}0$. It is found that all the variational schemes have fail points, at where the variational schemes fail to provide a lower energy (or a lower free energy at $T\ensuremath{\ne}0$) than the displaced-oscillator ground state and therefore the variational ground state becomes unstable, which results in a transition from a variational ground state to a displaced-oscillator ground state when the fail point is reached. Such transitions are always misidentified as crossover from a delocalized to localized phases in variational calculations, leading to an artifact of phonon-induced localization. Physics origin of the fail points and explanations for different transition behaviors with different spectral functions are found by studying the fail points of the variational schemes in the single-mode case.We present energy and free-energy analyses on all variational schemes used so far in the spin-boson model at both $T=0$ and $T\ensuremath{\ne}0$. It is found that all the variational schemes have fail points, at where the variational schemes fail to provide a lower energy (or a lower free energy at $T\ensuremath{\ne}0$) than the displaced-oscillator ground state and therefore the variational ground state becomes unstable, which results in a transition from a variational ground state to a displaced-oscillator ground state when the fail point is reached. Such transitions are always misidentified as crossover from a delocalized to localized phases in variational calculations, leading to an artifact of phonon-induced localization. Physics origin of the fail points and explanations for different transition behaviors with different spectral functions are found by studying the fail points of the variational schemes in the single-mode case.

arXiv:0705.1670Physical Review BAug 27, 20085 citations

The equilibrium thermodynamics of a spin-boson model

John T. Lewis, G. A. Raggio

Journal of Statistical PhysicsMar 1, 19889 citations

The equilibrium state of the spin Boson model

M. Fannes, Bruno Nachtergaele, André F. Verbeure

Jan 1, 19882 citations

Comment on “Coherent-incoherent transition in the sub-Ohmic spin-boson model”

Hang Wong, Zhide Chen

In a recent paper, Chin and Turlakov [Phys. Rev. B 73, 075311 (2006)] studied the sub-Ohmic spin-boson model at finite temperatures by using a variational method. The coherent-incoherent transition was found to be discontinuous, and the transition point was determined using the same method as that used for a continuous transition like in the Ohmic case at $T=0$ . In this Comment, we show that the transition point determined in this way is, according to the Landau theory of the first order transition, not thermodynamically the transition point, but just the point where the second minimum of the free energy begins to develop. The true transition point is determined by the condition that the free energy of the new phase becomes the global minimum. Based on this result, it is shown that the predicted reentrance phenomenon does not exist in practice.In a recent paper, Chin and Turlakov [Phys. Rev. B 73, 075311 (2006)] studied the sub-Ohmic spin-boson model at finite temperatures by using a variational method. The coherent-incoherent transition was found to be discontinuous, and the transition point was determined using the same method as that used for a continuous transition like in the Ohmic case at $T=0$. In this Comment, we show that the transition point determined in this way is, according to the Landau theory of the first order transition, not thermodynamically the transition point, but just the point where the second minimum of the free energy begins to develop. The true transition point is determined by the condition that the free energy of the new phase becomes the global minimum. Based on this result, it is shown that the predicted reentrance phenomenon does not exist in practice.

Physical Review BAug 30, 20074 citations

No-Go Theorem for Quasiparticle BEC in the Spin-Boson Model

Yoshitsugu Sekine

We analyze the possibility of Bose-Einstein condensation (BEC) at finite temperature in the spin-boson model within the frameworks of functional integral representations and the resolvent algebra. Because a sesquilinear form arising from the zero mode appears, analogous to the case of the free Bose gas, a BEC-type component is also formally present in the spin-boson model. However, according to arxiv:1207.4621, quasiparticles do not undergo BEC, so we have to exclude this possibility. A no-go theorem for BEC is obtained, but we find that the spin-boson model is not a model that follows the criterion in arxiv:1207.4621.We analyze the possibility of Bose-Einstein condensation (BEC) at finite temperature in the spin-boson model within the frameworks of functional integral representations and the resolvent algebra. Because a sesquilinear form arising from the zero mode appears, analogous to the case of the free Bose gas, a BEC-type component is also formally present in the spin-boson model. However, according to arxiv:1207.4621, quasiparticles do not undergo BEC, so we have to exclude this possibility. A no-go theorem for BEC is obtained, but we find that the spin-boson model is not a model that follows the criterion in arxiv:1207.4621.

arXiv:2604.27904Apr 30, 20260 citations

We present energy and free-energy analyses on all variational schemes used so far in the spin-boson model at both

T=0

and $T\ensuremath{\ne}0$. It is found that all the variational schemes have fail points, at where the variational schemes fail to provide a lower energy (or a lower free energy at $T\ensuremath{\ne}0$) than the displaced-oscillator ground state and therefore the variational ground state becomes unstable, which results in a transition from a variational ground state to a displaced-oscillator ground state when the fail point is reached. Such transitions are always misidentified as crossover from a delocalized to localized phases in variational calculations, leading to an artifact of phonon-induced localization. Physics origin of the fail points and explanations for different transition behaviors with different spectral functions are found by studying the fail points of the variational schemes in the single-mode case.

T=0

. In this Comment, we show that the transition point determined in this way is, according to the Landau theory of the first order transition, not thermodynamically the transition point, but just the point where the second minimum of the free energy begins to develop. The true transition point is determined by the condition that the free energy of the new phase becomes the global minimum. Based on this result, it is shown that the predicted reentrance phenomenon does not exist in practice.