| The paradigmatic model for a simple quantum mechanical degree of freedom coupled to a dissipative bath is the spin-boson model. Its partition function can be expressed as a path integral over imaginary time world lines of an Ising spin in a transverse field with a weight that contains retarded self-interactions decaying algebraically in time. We developped and implemented a continuous imaginary time cluster algorithm that samples directly this path integral without Trotter-discretization and applied it to various forms of the bath spectral function. Thermodynamic quantities can be calculated to arbitrary precision and the universal properties of the localization transition at zero tempertaure can be extracted via conventional "finite temperature" scaling. We find that this quantum phase transition, occurring at a critical spin-bath coupling strength, is for all low frequency powers s of the spectral function in the same universality class as the classical Ising chain with 1/r(1+s) long range interactions, which is at variance with a recent RG prediction. |
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