Two-state system coupled to phonons: A renormalization-group analysis of the transition

Abstract

We present a systematic renormalization-group analysis of the transition occurring in a symmetric two-state system with a linear dissipative coupling to a heat bath. We define the theory as a double expansion in $\Delta$ (tunneling frequency) and $\delta$ (distance from the critical coupling to the heat bath at $\Delta =0\mathrm{}$), following a similar strategy as in the sine-Gordon theory. We reproduce previous results and obtain higher-order terms and a new universal correction in the flow equations.