Anomalous scaling of conductivity in integrable fermion systems

TL;DR

This paper investigates the high-temperature electrical conductivity in one-dimensional integrable fermion models, revealing anomalous finite-size effects and suggesting a finite d.c. conductivity in the thermodynamic limit.

Contribution

It provides new insights into the conductivity behavior of integrable fermion systems, combining numerical and analytical methods to explore finite-size effects and the potential for finite d.c. conductivity.

Findings

Finite-size effects cause large anomalies at low frequencies.

Finite d.c. conductivity is indicated by frequency-moment analysis.

Results suggest a possible finite d.c. conductivity in the thermodynamic limit.

Abstract

We analyze the high-temperature conductivity in one-dimensional integrable models of interacting fermions: the t-V model (anisotropic Heisenberg spin chain) and the Hubbard model, at half-filling in the regime corresponding to insulating ground state. A microcanonical Lanczos method study for finite size systems reveals anomalously large finite-size effects at low frequencies while a frequency-moment analysis indicates a finite d.c. conductivity. This phenomenon also appears in a prototype integrable quantum system of impenetrable particles, representing a strong-coupling limit of both models. In the thermodynamic limit, the two results could converge to a finite d.c. conductivity rather than an ideal conductor or insulator scenario.