Scaling and universality in the anisotropic Kondo model and the dissipative two-state system

TL;DR

This paper investigates the universal scaling behavior of the Ohmic two-state system by leveraging its equivalence to the anisotropic Kondo model, providing universal functions for key physical quantities dependent on dissipation strength.

Contribution

It introduces universal scaling functions for the Ohmic two-state system's thermodynamic and dynamical properties, explicitly linking them to the dissipation strength and renormalized tunneling frequency.

Findings

Universal scaling functions for specific heat, susceptibility, and spin relaxation.

Dependence of scaling functions on dissipation strength and renormalized tunneling.

Method to extract dissipation parameters from experimental data.

Abstract

Scaling and universality in the Ohmic two-state system is investigated by exploiting the equivalence of this model to the anisotropic Kondo model. For the Ohmic two-state system, we find universal scaling functions for the specific heat, $C_{\alpha}(T)$, static susceptibility, $\chi_{\alpha}(T)$, and spin relaxation function $S_{\alpha}(\omega)$ depending on the reduced temperature $T/\Delta_{r}$ (frequency $\omega/\Delta_{r}$), with $\Delta_{r}$ the renormalized tunneling frequency, and uniquely specified by the dissipation strength $\alpha$ ($0<\alpha<1$). The scaling functions can be used to extract $\alpha$ and $\Delta_{r}$ in experimental realizations.