Spectra of the Dissipative Spin Chain

This paper generalizes the (0+1)-dimensional spin-boson problem to the corresponding (1+1)-dimensional version. Monte Carlo simulation is used to find the phase diagram and imaginary time correlation function. The real frequency spectrum is recovered by the newly developed P\'ade regression analytic continuation method. We find that, as dissipation strength $\alpha$ is increased, the sharp quasi-particle spectrum is broadened and the peak frequency is lower. According to the behavior of the low frequency spectrum, we classify the dynamical phase into three different regions: weakly damped, linear $k$-edge, and strongly damped.