Conductivity in the Heisenberg chain with next to nearest neighbor interaction

TL;DR

This paper rigorously proves that a perturbed XXZ spin chain with next-nearest neighbor interactions exhibits ideal metallic behavior with infinite conductivity, maintaining key properties despite breaking integrability.

Contribution

It provides a rigorous proof of infinite conductivity in a non-integrable spin chain using Exact Renormalization Group methods, accounting for lattice symmetries.

Findings

Infinite conductivity (Drude weight) is strictly positive at zero temperature.

The Drude weight satisfies the same relations as in the integrable case.

Irrelevant terms are crucial for preserving lattice symmetries.

Abstract

We consider a spin chain given by the XXZ model with a weak next to nearest neighbor perturbation which breaks its exact integrability. We prove that such system has an ideal metallic behavior (infinite conductivity), by rigorously establishing strict lower bounds on the zero temperature Drude weight which are strictly positive. The proof is based on Exact Renormalization Group methods allowing to prove the convergence of the expansions and to fully take into account the irrelevant terms, which play an essential role in ensuring the correct lattice symmetries. We also prove that the Drude weight verifies the same parameter-free relations as in the absence of the integrability breaking perturbation.