Transport in a one-dimensional isotropic Heisenberg model at high temperature

Lyudvig Dmitrievich Faddeev, Leon Armenovich Takhtadzhyan

Marko Žnidarič

Magnetization transport in a one-dimensional isotropic spin 1/2 Heisenberg model is studied. It is shown that in a nonequilibrium steady state at high temperature and constant small driving the magnetization current depends on the system length L as ∼ 1/ L 0.5 , meaning that the diffusion constant diverges as ∼ L 0.5 . Spectral properties of a superoperator governing the relaxation towards a nonequilibrium steady state are also discussed.

L. D. Faddeev, Leon Armenovich Takhtadzhyan

Marko Žnidarič

We analytically and numerically study spin transport in a one-dimensional Heisenberg model in linear-response regime at infinite temperature. It is shown that as the anisotropy parameter Δ is varied spin transport changes from ballistic for Δ<1 to anomalous at the isotropic point Δ=1, to diffusive for finite Δ>1, ending up as a perfect isolator in the Ising limit of infinite Δ. Using perturbation theory for large Δ a quantitative prediction is made for the dependence of diffusion constant on Δ.

Enej Ilievski, Jacopo De Nardis, Marko Medenjak +1 more

We identify a class of one-dimensional spin and fermionic lattice models that display diverging spin and charge diffusion constants, including several paradigmatic models of exactly solvable, strongly correlated many-body dynamics such as the isotropic Heisenberg spin chains, the Fermi-Hubbard model, and the t-J model at the integrable point. Using the hydrodynamic transport theory, we derive an analytic lower bound on the spin and charge diffusion constants by calculating the curvature of the corresponding Drude weights at half-filling, and demonstrate that for certain lattice models with isotropic interactions some of the Noether charges exhibit superdiffusive transport at finite temperature and half-filling.

David W. Wood