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arXiv:1406.2799 · Physical Review B

Scaling of diffusion constants in the spin- 12 XX ladder

Robin Steinigeweg, Fabian Heidrich‐Meisner, Jochen Gemmer B, Kristel F. L. Michielsen, Hans A. De Raedt

Published Sep 25, 2014• 45 citations
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Abstract

We study the dynamics of spin currents in the spin-$\frac{1}{2}$ XX ladder at finite temperature. Within linear response theory, we numerically calculate autocorrelation functions for quantum systems larger than what is accessible with exact diagonalization using the concept of dynamical quantum typicality. While the spin Drude weight vanishes exponentially quickly with increasing system size, we show that this model realizes standard diffusive dynamics. Moreover, we unveil the existence of three qualitatively different dependencies of the spin-diffusion coefficient on the rung-coupling strength, resulting from a crossover from exponential to Gaussian dissipation as the rung coupling increases, in agreement with analytical predictions. We further discuss the implications of our results for experiments with cold atomic gases.

DOI
10.1103/physrevb.90.094417

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We study the dynamics of spin currents in the spin-12\frac{1}{2}21​ XX ladder at finite temperature. Within linear response theory, we numerically calculate autocorrelation functions for quantum systems larger than what is accessible with exact diagonalization using the concept of dynamical quantum typicality. While the spin Drude weight vanishes exponentially quickly with increasing system size, we show that this model realizes standard diffusive dynamics. Moreover, we unveil the existence of three qualitatively different dependencies of the spin-diffusion coefficient on the rung-coupling strength, resulting from a crossover from exponential to Gaussian dissipation as the rung coupling increases, in agreement with analytical predictions. We further discuss the implications of our results for experiments with cold atomic gases.
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Time-dependent spin-autocorrelation functions at T=\ensuremath{\infty} and (in particular) their spectral densities for the bulk spin and the boundary spin of the semi-infinite spin-1/2 XXZ model (with exchange parameters Jx{\mathit{J}}_{\mathit{x}}Jx​=Jy{\mathit{J}}_{\mathit{y}}Jy​\ensuremath{\equiv}J, Jz{\mathit{J}}_{\mathit{z}}Jz​) are investigated on the basis of (i) rigorous bounds in the time domain and (ii) a continued-fraction analysis in the frequency domain. We have found strong numerical evidence for spin diffusion in quantum spin models. For Jz{\mathit{J}}_{\mathit{z}}Jz​/J increasing from zero, the results of the short-time expansion indicate a change of the bulk-spin xx-autocorrelation function from Gaussian decay to exponential decay. The continued-fraction analysis of the same dynamic quantity signals a change from exponential decay to power-law decay as Jz{\mathit{J}}_{\mathit{z}}Jz​/J approaches unity and back to a more rapid decay upon further increase of that parameter. By contrast, the change in symmetry at Jz{\mathit{J}}_{\mathit{z}}Jz​/J=1 has virtually no impact on the bulk-spin zz-autocorrelation function (as expected). Similar contrasting properties are observable in the boundary-spin autocorrelation functions.