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Thermodyamic Bounds on Drude Weights in Terms of Almost-conserved Quantities

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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 (Prosen, in Phys Rev Lett 106:217206, 2011).

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Authors and Affiliations

  1. Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia

    Enej Ilievski & Tomaž Prosen

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  1. Enej Ilievski
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  2. Tomaž Prosen
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Correspondence to Tomaž Prosen.

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Communicated by H. Spohn

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Ilievski, E., Prosen, T. Thermodyamic Bounds on Drude Weights in Terms of Almost-conserved Quantities. Commun. Math. Phys. 318, 809–830 (2013). https://doi.org/10.1007/s00220-012-1599-4

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  • DOI: https://doi.org/10.1007/s00220-012-1599-4

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