We consider a spin chain given by the XXZ model with a weak next-to-nearest-neighbor perturbation that breaks its exact integrability. We prove that such a 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 us 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.

Conductivity in the Heisenberg chain with next-to-nearest-neighbor interaction / V. Mastropietro. - In: PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. - ISSN 1539-3755. - 87:4(2013 Apr 25), pp. 042121.1-042121.8.

Conductivity in the Heisenberg chain with next-to-nearest-neighbor interaction

V. Mastropietro
2013-04-25

Abstract

We consider a spin chain given by the XXZ model with a weak next-to-nearest-neighbor perturbation that breaks its exact integrability. We prove that such a 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 us 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.
Settore MAT/07 - Fisica Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/222247
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