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 verifies the same parameter-free relations as in the absence of the integrability breaking perturbation.

References in corpus (6)

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• Conservation laws, integrability and transport in one-dimensional quantum systems
• Absence of interaction corrections in graphene conductivity
• Spin conductivity in almost integrable spin chains
• Finite Drude weight for 1D low temperature conductors
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Cited by in corpus (6)

• Finite-temperature transport in one-dimensional quantum lattice models
• Quantum Quench for inhomogeneous states in the non-local Luttinger model
• Canonical Drude weight for non-integrable quantum spin chains
• Giant rectification in segmented, strongly interacting, spin chains despite the presence of perturbations
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Vanishing of Drude weight in interacting fermions on Zd with quasi-periodic disorder