Dynamic correlations of antiferromagnetic spin- XXZ chains at arbitrary temperature from complete diagonalization

Abstract

All eigenstates and eigenvalues are determined for the spin-1 2 XXZ chain Hϭ2J͚ i (S i x S iϩ1for rings with up to Nϭ16 spins, for anisotropies ⌬ϭ0, cos(0.3), and 1. The dynamic spin pair correlations ͗S lϩn (t)S l ͘, (ϭx,z), the dynamic structure factors S (q,), and the intermediate structure factors I (q,t) are calculated for arbitrary temperature T. It is found that for all T, S z (q,) is mainly concentrated on the region ͉͉Ͻ 2 (q), where 2 (q) is the upper boundary of the two-spinon continuum, although excited states corresponding to a much broader frequency spectrum contribute. This is also true for the Haldane-Shastry model and the frustrated Heisenberg model. The intermediate structure factors I (q,t) for ⌬ 0 show exponential decay for high T and large q. Within the accessible time range, the time-dependent spin-correlation functions do not display the long-time signatures of spin diffusion.Approximate analytic expressions for the Tϭ0 dynamic structure factors were conjectured, which take into account known sum rules as well as exact results for the case ⌬ϭ0 and asymptotic results ͑2.5͒ for small q and .

Conductivity of quantum spin chains: A quantum Monte Carlo approach

“…Evidence for ballistic (or quasi-ballistic) magnetization transport have been found in recent exact diagonalization studies 6 of H (xxz) at high temperatures 7,8 . A connection between integrability, conservation laws and ballistic transport has been proposed by Zotos and coworkers [9][10][11][12]7 .…”

“…The response to the time-integrated twist is then obtained from (8) and the dynamical conductivity takes the usual form…”

Conservation laws, integrability, and transport in one-dimensional quantum systems

“…For decades, a great deal of effort has been made to compute the autocorrelation function for the XXZ model with general values of anisotropy, particularly for the Heisenberg model. [44][45][46][47][48][49][50] While ED is always limited to small systems and short times (out to t ∼ 6 in units of inverse exchange constant for L = 16 sites), 48 QMC 49 is plagued by the analytic continuation and cannot resolve singularities associated with the long-time behavior. Although the more recently developed density matrix renormalization group (DMRG) method applied to the transfer matrix 51 works directly in the thermodynamic limit, it is also restricted to intermediate times and has not detected a diffusive contribution at low temperatures.…”

Time-dependent correlations in quantum magnets at finite temperature

“…The concomitant asymmetry cannot be described by a pure Lorentzian at finite temperatures. Hence, the details of the scattering processes have a considerable impact on the correlations, and more sophisticated theories have been employed to explain this phenomenon [10,[12][13][14][15][16][17][18][19][20][21][22].…”