Towards a statistical theory of transport by strongly-interacting lattice fermions

TL;DR

This paper investigates high-temperature electric transport in a model of strongly interacting spinless fermions, revealing non-trivial conductivity behavior linked to long-time current correlations and nonlinear mode couplings.

Contribution

It introduces a statistical approach to analyze transport in a nonrandom, strongly interacting fermion model, connecting spectral properties to conductivity behavior.

Findings

Conductivity exhibits a non-divergent singularity at zero frequency.

Current autocorrelation shows a power-law long-time tail.

Model behaves like a Gaussian random matrix ensemble.

Abstract

We present a study of electric transport at high temperature in a model of strongly interacting spinless fermions without disorder. We use exact diagonalization to study the statistics of the energy eigenvalues, eigenstates, and the matrix elements of the current. These suggest that our nonrandom Hamiltonian behaves like a member of a certain ensemble of Gaussian random matrices. We calculate the conductivity $\sigma(\omega)$ and examine its behavior, both in finite size samples and as extrapolated to the thermodynamic limit. We find that $\sigma(\omega)$ has a prominent non-divergent singularity at $\omega=0$ reflecting a power-law long-time tail in the current autocorrelation function that arises from nonlinear couplings between the long-wavelength diffusive modes of the energy and particle number.