Lower bounds on high-temperature diffusion constants from quadratically extensive almost conserved operators
arXiv:1310.8629 · doi:10.1103/PhysRevE.89.012142
Abstract
We prove a general theorem which provides a strict lower bound on high-temperature Green-Kubo diffusion constants in locally interacting quantum lattice systems, under the assumption of existence of a quadratically extensive almost conserved quantity - an operator whose commutator with the lattice Hamiltonian is localized on the boundary sites only. We explicitly demonstrate and compute such a bound in two important models in one dimension, namely in the (isotropic) Heisenberg spin 1/2 chain and in the fermionic Hubbard chain.
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