Spin and energy transport in spin-\textonehalf{} anisotropic magnetic chains with nearest-neighbor interactions are studied in the high-temperature limit. The analysis is based on a calculation of the zeroth, second, and fourth moments of the Fourier transforms of the spin and energy density correlation functions. Spin diffusion is predicted for sufficiently small values of the wave vector, except in the
XY limit. Energy transport is nondiffusive for all values of the wave vector. Energy diffusion is predicted for chains with isotropic nearest-neighbor interactions and spin greater than \textonehalf{} as well as for spin-\textonehalf{} two-dimensional square lattices and three-dimensional simple and body-centered cubic lattices having isotropic nearest-neighbor interactions.
It is well established that at zero magnetic field
h=0, the spin diffusion constant of the spin-
21 XXZ chain is for anisotropy $\mathrm{\ensuremath{\Delta}}>1$ finite for both low and high temperatures, implying that the type of spin transport is normal diffusive. Although it is expected that this holds for all finite temperatures
T>0, the calculation of the spin diffusion constant for all
T is typically intractable. Here we consider a class of energy eigenstates that exist both for anisotropies $\mathrm{\ensuremath{\Delta}}=1$ and $\mathrm{\ensuremath{\Delta}}>1$. We show that at the isotropic point their contributions are behind the diffusion constant being infinite, spin transport being anomalous superdiffusive for
T>0. That for $\mathrm{\ensuremath{\Delta}}>1$ such states do not contribute to the diffusion constant is shown to imply it is finite, spin transport being normal diffusive for
T>0. By combining the connection through a Jordan-Wigner transformation of the spin-
21 XXZ chain to the one-dimensional (1D) lattice spinless fermion model at zero chemical potential $\ensuremath{\mu}=0$, for $V/J\ensuremath{\ge}1$ with its Bethe-ansatz solution, where
V is the nearest-neighbor Coulomb repulsion and
J=2t is twice the hopping integral
t, in this paper we also address the issue of the
T>0 charge transport of that model at $\ensuremath{\mu}=0$. It is found to be anomalous superdiffusive for
V/J=1 and normal diffusive for
V/J>1. Our results thus open the door to a key advance in the understanding for all finite temperatures
T>0 of the spin transport in the spin-
21 XXZ chain at
h=0 for anisotropy $\mathrm{\ensuremath{\Delta}}\ensuremath{\ge}1$ and of the charge transport in the 1D lattice spinless fermion model at $\ensuremath{\mu}=0$ for $V/J\ensuremath{\ge}1$.
The studies of this paper on the spin- 1 / 2 XXZ chain at finite temperatures T > 0 have two complementary goals. The first is to identify the spin carriers of all its S q > 0 energy eigenstates and to show that their spin elementary currents fully control the spin-transport quantities. Here, S q is the q -spin of the continuous S U q ( 2 ) symmetry of the model for anisotropy Δ > 1 . To achieve this goal, our studies rely on a suitable exact valid in throughout the Hilbert space and associated with normal spin operators, rather than fractionalized particles such as spinons. Both the spin stiffness and the zero-field spin-diffusion constant are expressed in terms of thermal expectation values of the square of the elementary currents carried by the spin carriers. Our second goal is to confirm that the zero-field and finite-temperature spin transport is normal diffusive for Δ > 1 . We use two complementary methods that rely on an inequality for the T > 0 spin stiffness and the above thermal expectation values, respectively, to show that the contributions to ballistic spin transport vanish. Complementarily, for T > 0 and Δ > 1 , the spin-diffusion constant is found to be finite and enhanced upon lowering T , reaching its largest yet finite values at low temperatures. Evidence suggests that it diverges in the Δ → 1 limit for T > 0 , consistent with T > 0 anomalous superdiffusive spin transport at Δ = 1 and zero field.
We study magnetization transport at infinite temperature in several spin ladder systems as well as in next-nearest-neighbor coupled spin chains. In the integrable ladder considered we analytically show that the transport is ballistic in sectors with nonzero average magnetization, while numerical simulations of a nonequilibrium stationary setting indicate an anomalous transport in the zero-magnetization sector. For other systems, isotropic Heisenberg ladder and spin chains, showing eigenlevel repulsion typical of quantum chaotic systems, numerical simulations indicate diffusive transport.
We study energy transport in disordered
XXZ spin-1/2 chains driven to nonequilibrium configurations by thermal reservoirs of different temperatures at the boundaries, using large-scale matrix product simulations. In particular we discuss the transition between diffusive and subdiffusive transport in sectors of zero and finite magnetization at high temperature. At large anisotropies we find that diffusive energy transport prevails over a large range of disorder strengths, which is in contrast to spin transport that is subdiffusive in the same regime for weak disorder. However, at finite magnetization both energy and spin currents decay as a function of the system size with the same exponent. We conclude that diffusion of energy is much more pervasive than that of magnetization in these disordered spin-1/2 systems, and occurs across a significant range of the interaction-disorder parameter phase space. We support the existence of this asymmetry, reminiscent of that in the clean limit, by an analytical estimation of diffusion constants for weak disorder.
We investigate transport in several translationally invariant spin-
21 chains in the limit of high temperatures. We concretely consider spin transport in the anisotropic Heisenberg chain, the pure Heisenberg chain within an alternating field, and energy transport in an Ising chain which is exposed to a tilted field. Our approach is essentially based on a connection between the evolution of the variance of an inhomogeneous nonequilibrium density and the current-autocorrelation function at finite times. Although this relationship is not restricted to the case of diffusive transport, it allows to extract a quantitative value for the diffusion constant in that case. By means of numerically exact diagonalization we indeed observe diffusive behavior in the considered spin chains for a range of model parameters and confirm the diffusion coefficients which were obtained for these systems from nonequilibrium bath scenarios.