The effectiveness of the variational approach à la Feynman is proved in the spin-boson model, i.e., the simplest realization of the Caldeira-Leggett model able to reveal the quantum phase transition from delocalized to localized states and the quantum dissipation and decoherence effects induced by a heat bath. After exactly eliminating the bath degrees of freedom, we propose a trial, nonlocal in time, interaction between the spin and itself simulating the coupling of the two-level system with the bosonic bath. It stems from a Hamiltonian where the spin is linearly coupled to a finite number of harmonic oscillators whose frequencies and coupling strengths are variationally determined. We show that a very limited number of these fictitious modes is enough to get a remarkable agreement, up to very low temperatures, with the data obtained by using an approximation-free Monte Carlo approach, predicting (1) in the Ohmic regime, a Berezinski-Thouless-Kosterlitz quantum phase transition exhibiting the typical universal jump at the critical value; and (2) in the sub-Ohmic regime (s?0.5), mean-field quantum phase transitions, with logarithmic corrections for s=0.5.
Quantum phase transitions in the spin-boson model: Monte Carlo method versus variational approach à la Feynman / De Filippis, G.; De Candia, A.; Cangemi, L. M.; Sassetti, M.; Fazio, R.; Cataudella, V.. - In: PHYSICAL REVIEW. B. - ISSN 2469-9950. - 101:18(2020). [10.1103/PHYSREVB.101.180408]
Quantum phase transitions in the spin-boson model: Monte Carlo method versus variational approach à la Feynman
De Filippis G.;De Candia A.;Cangemi L. M.;Sassetti M.;Fazio R.;Cataudella V.
2020
Abstract
The effectiveness of the variational approach à la Feynman is proved in the spin-boson model, i.e., the simplest realization of the Caldeira-Leggett model able to reveal the quantum phase transition from delocalized to localized states and the quantum dissipation and decoherence effects induced by a heat bath. After exactly eliminating the bath degrees of freedom, we propose a trial, nonlocal in time, interaction between the spin and itself simulating the coupling of the two-level system with the bosonic bath. It stems from a Hamiltonian where the spin is linearly coupled to a finite number of harmonic oscillators whose frequencies and coupling strengths are variationally determined. We show that a very limited number of these fictitious modes is enough to get a remarkable agreement, up to very low temperatures, with the data obtained by using an approximation-free Monte Carlo approach, predicting (1) in the Ohmic regime, a Berezinski-Thouless-Kosterlitz quantum phase transition exhibiting the typical universal jump at the critical value; and (2) in the sub-Ohmic regime (s?0.5), mean-field quantum phase transitions, with logarithmic corrections for s=0.5.File | Dimensione | Formato | |
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