Viscosity Sum Rules at Large Scattering Lengths

TL;DR

This paper derives model-independent sum rules for shear and bulk viscosities in strongly interacting fermionic systems using OPE and dispersion relations, linking viscosities to the Tan contact parameter across all scattering lengths.

Contribution

It introduces new Borel-resummed sum rules for viscosities that are valid at arbitrary scattering lengths and relate them directly to the Tan contact parameter C(a).

Findings

Sum rules connect viscosities to Tan contact C(a).

Results valid for all scattering lengths with small operator corrections.

Sum rules can be optimized for low-energy data analysis.

Abstract

We use the operator product expansion (OPE) and dispersion relations to obtain new model-independent "Borel-resummed" sum rules for both shear and bulk viscosity of many-body systems of spin-1/2 fermions with predominantly short range S-wave interactions. These sum rules relate Gaussian weights of the frequency-dependent viscosities to the Tan contact parameter C(a). Our results are valid for arbitrary values of the scattering length a, but receive small corrections from operators of dimension larger than 5 in the OPE, and can be used to study transport properties in the vicinity of the infinite scattering length fixed point. In particular, we find that the exact dependence of the shear viscosity sum rule on scattering length is controlled by the function C(a). The sum rules that we obtain depend on a frequency scale w that can be optimized to maximize their overlap with low-energy data.