Quantum Tricritical Point in the Spin-Boson Model with an Ohmic Bath

The dynamics of the spin-boson model with an Ohmic bath at finite temperature is studied by a variational calculation. Numerical solution of the self-consistent equation derived from the variational method shows that the transition from incoherent to coherent phases is discontinuous. It indicates that （T = 0, s = 1） is a tricritical point, i.e. the transition changes from continuous to discontinuous by tuning from T = 0 to T≠ 0. The discontinuous transition at finite temperature is analysed by Landau theory and the relation to the experimental observation on the coherent state is also discussed.