Equilibrium Dynamics of the Sub-Ohmic Spin-boson Model At Finite Temperature

TL;DR

This paper employs the full-density matrix NRG method to analyze the equilibrium dynamical correlations of the sub-Ohmic spin-boson model at finite temperature, revealing temperature-dependent spectral features and deviations from zero-temperature power laws.

Contribution

It introduces a detailed finite-temperature analysis of the sub-Ohmic spin-boson model using FDM-NRG, highlighting temperature effects on spectral functions.

Findings

Identification of a temperature-dependent peak at ω_T ~ T

Merging of finite-temperature and zero-temperature curves at high frequencies

Deviation from zero-temperature power-law behavior at low frequencies

Abstract

We use the full-density matrix (FDM) numerical renormalization group (NRG) method to calculate the equilibrium dynamical correlation function $C(\omega)$ of the spin operator $\sigma_z$ at finite temperature for the sub-Ohmic spin-boson model. A peak is observed at the frequency $\omega_{T}\sim T$ in the curve of $C(\omega)$. The curve merges with the zero temperature $C(\omega)$ in $\omega \gg \omega_{T}$ and deviate significantly from the power-law form $\omega^{\pm s}$ of the zero temperature curve in $\omega \ll\omega_{T}$.