Thermodyamic bounds on Drude weights in terms of almost-conserved quantities

Abstract

We consider one-dimensional translationally invariant quantum spin (or fermionic) lattices and prove a Mazur-type inequality bounding the time-averaged thermodynamic limit of a finite-temperature expectation of a spatio-temporal autocorrelation function of a local observable in terms of quasi-local conservation laws with open boundary conditions. Namely, the commutator between the Hamiltonian and the conservation law of a finite chain may result in boundary terms only. No reference to techniques used in Suzuki's proof of Mazur bound is made (which strictly applies only to finite-size systems with exact conservation laws), but Lieb-Robinson bounds and exponential clustering theorems of quasi-local C^* quantum spin algebras are invoked instead. Our result has an important application in the transport theory of quantum spin chains, in particular it provides rigorous non-trivial examples of positive finite-temperature spin Drude weight in the anisotropic Heisenberg XXZ spin 1/2 chain [Phys. Rev. Lett. 106, 217206 (2011)].

version as accepted by Communications in Mathematical Physics (22 pages with 2 pdf-figures)

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• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Propagation of Correlations in Quantum Lattice Systems
• Drude weight in systems with open boundary conditions

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