Authors: Vieri Mastropietro

Title: Conductivity in the Heisenberg chain with next to nearest neighbor interaction
 
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 veries the same parameter-free relations as in the absence of the integrability breaking perturbation.

Keywords: quantum spin chain, XXZ model, conductivity, Drude weight, Ward identities, renormalization group

Vieri Mastropietro
Dipartimento di Matematica
Università di Milano
Via Saldini, 50, I-20133 Milano - ITALY
e-mail: Vieri DOT Mastropietro AT unimi DOT it