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Real-time dynamics in spin-12 chains with adaptive time-dependent density matrix renormalization group

Dominique Gobert1,2, Corinna Kollath1,2, Ulrich Schollwöck1, and Gunter Schütz3

  • 1Institute for Theoretical Physics C, RWTH Aachen, D-52056 Aachen, Germany
  • 2Physics Department and CeNS, LMU München, Theresienstrasse 37, D-80333 München, Germany
  • 3Institut für Festkörperforschung, Forschungszentrum Jülich, D-52425 Jülich, Germany

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Phys. Rev. E 71, 036102 – Published 3 March, 2005

DOI: https://doi.org/10.1103/PhysRevE.71.036102

Abstract

We investigate the influence of different interaction strengths and dimerizations on the magnetization transport in antiferromagnetic spin 1∕2XXZ chains. We focus on the real-time evolution of the inhomogeneous initial state ∣↑⋯↑↓⋯↓⟩ in using the adaptive time-dependent density-matrix renormalization group (adaptive t-DMRG). Time scales accessible to us are of the order of 100 units of time measured in ℏ∕J for almost negligible error in the observables. We find ballistic magnetization transport for small SzSz interaction and arbitrary dimerization, but almost no transport for stronger SzSz interaction, with a sharp crossover at Jz=1. Additionally, we perform a detailed analysis of the error made by the adaptive time-dependent DMRG using the fact that the evolution in the XX model is known exactly. We find that the error at small times is dominated by the error made by the Trotter decomposition, whereas for longer times the DMRG truncation error becomes the most important, with a very sharp crossover at some “runaway” time. Overall, errors are extremely small before the “runaway” time.

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Phys. Rev. E 71, 036102– Published 3 March, 2005
  • Received 7 October 2004

© 2005 American Physical Society

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