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Quantum phase transitions in the sub-ohmic spin-boson model: Failure of the quantum-classical mapping

Matthias Vojta·Ning-Hua Tong·Ralf Bulla
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Abstract

The effective theories for many quantum phase transitions can be mapped onto those of classical transitions. Here we show that such a mapping fails for the sub-ohmic spin-boson model which describes a two-level system coupled to a bosonic bath with power-law spectral density, J(omega) ~ omega^s. Using an epsilon expansion we prove that this model has a quantum transition controlled by an interacting fixed point at small s, and support this by numerical calculations. In contrast, the corresponding classical long-range Ising model is known to have an upper-critical dimension at s = 1/2, with mean-field transition behavior controlled by a non-interacting fixed point for 0 < s < 1/2. The failure of the quantum-classical mapping is argued to arise from the long-ranged interaction in imaginary time in the quantum model.

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Matthias Vojta, Ning-Hua Tong, Ralf Bulla. 2009-06-08. Quantum phase transitions in the sub-ohmic spin-boson model: Failure of the quantum-classical mapping. https://doi.org/10.1103/physrevlett.94.070604

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