title: Quantum phase transitions in the sub-Ohmic spin-boson model: failure of the quantum-classical mapping.
abstract: The effective theories for many quantum phase transitions can be mapped onto those of classical transitions. Here we show that the naive 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) proportional, variantomega(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 display mean-field transition behavior for 0 < s < 1/2, controlled by a noninteracting fixed point. The failure of the quantum-classical mapping is argued to arise from the long-ranged interaction in imaginary time in the quantum model.
authors.affiliation: Institut für Theorie der Kondensierten Materie, Universität Karlsruhe, 76128 Karlsruhe, Germany.
authors.forename: Matthias
authors.initials: M
authors.lastname: Vojta
authors.forename: Ning-Hua
authors.initials: NH
authors.lastname: Tong
authors.forename: Ralf
authors.initials: R
authors.lastname: Bulla