# Spectra of the Dissipative Spin Chain

## TL;DR

This study extends the spin-boson model to a (1+1)-dimensional system, using Monte Carlo simulations and a novel Pade regression method to analyze how dissipation affects the spectral properties and phase behavior.

## Contribution

It introduces a (1+1)-dimensional spin chain model and develops a Pade regression technique for spectral analysis, advancing understanding of dissipative quantum systems.

## Key findings

- Dissipation broadens the quasi-particle spectrum.
- Peak frequency decreases with increased dissipation.
- Identifies three dynamical phases based on spectral behavior.

## Abstract

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.