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

TL;DR

This paper establishes a new bound on the autocorrelation functions in quantum spin chains using quasi-local conservation laws, with implications for understanding spin transport and Drude weights at finite temperature.

Contribution

It introduces a Mazur-type inequality based on quasi-local conservation laws, avoiding finite-size limitations and applying Lieb-Robinson bounds and clustering theorems.

Findings

Proves a bound on autocorrelation functions in quantum spin chains.

Demonstrates positive finite-temperature spin Drude weight in the XXZ model.

Provides rigorous support for spin transport properties at finite temperature.

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)].