Thermodynamics of the dissipative two-state system: a Bethe Ansatz study

TL;DR

This paper provides an exact thermodynamic analysis of the dissipative two-state system across all temperatures and asymmetries by leveraging its equivalence to the anisotropic Kondo model, revealing universal scaling functions and temperature behaviors.

Contribution

It introduces an exact Bethe Ansatz solution for the thermodynamics of the dissipative two-state system, including universal scaling functions for various dissipation strengths.

Findings

Universal scaling functions for specific heat and susceptibility are derived.

Logarithmic corrections at high temperatures near the Kondo limit are identified.

Low temperature behavior always exhibits Fermi liquid characteristics.

Abstract

The thermodynamics of the dissipative two-state system is calculated exactly for all temperatures and level asymmetries for the case of Ohmic dissipation. We exploit the equivalence of the two-state system to the anisotropic Kondo model and extract the thermodynamics of the former by solving the thermodynamic Bethe Ansatz equations of the latter. The universal scaling functions for the specific heat $C_{\alpha}(T)$ and static dielectric susceptibility $\chi_{\alpha}(T)$ are extracted for all dissipation strengths $0<\alpha<1$ for both symmetric and asymmetric two-state systems. The logarithmic corrections to these quantities at high temperatures are found in the Kondo limit $\alpha\to 1^{-}$, whereas for $\alpha< 1$ we find the expected power law temperature dependences with the powers being functions of the dissipative coupling $\alpha$. The low temperature behaviour is always that of a Fermi liquid.