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arXiv:cond-mat/0702059 · Journal of Physics A Mathematical and Theoretical

Transport of interface states in the Heisenberg chain

Tom Michoel, Bruno Nachtergaele, Wolfgang Spitzer

Published Oct 29, 2008• 3 citations
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Abstract

We demonstrate the transport of interface states in the one-dimensional ferromagnetic Heisenberg model by a time-dependent magnetic field. Our analysis is based on the standard adiabatic theorem. This is supplemented by a numerical analysis via the recently developed time-dependent density matrix renormalization group method, where we calculate the adiabatic constant as a function of the strength of the magnetic field and the anisotropy of the interaction.

DOI
10.1088/1751-8113/41/49/492001

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We present a variational approach to the Heisenberg antiferromagnetic model for spin 1/2 and anisotropic exchange, with an external longitudinal and transverse magnetic field. In the one-dimensional case, we calculate exactly with our trial function the expectation values of energy, sublattice magnetization, and magnetic susceptibility. On minimizing the energy, we obtain several phases, which depend on the strength of the field and anisotropy parameter. Subsequently we approach the problem numerically and solve it for a chain of 12 spins using the Lanczos method. The two approaches are in excellent concordance, particularly for the critical fields of the transitions, over a wide range of the parameters of the model. Beside its precision and mathematical simplicity, the method has the important advantage of accounting for the different magnetic phases and their transitions with a single trial function that has a compact mathematical expression. The formalism is expected to work better in higher dimensions, but the corresponding calculations are omitted because of the lack of numerical field-dependent data with which to compare.
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We propose an easily implemented approach to study time-dependent correlation functions of one-dimensional systems at finite-temperature T using the density matrix renormalization group. The entanglement growth inherent to any time-dependent calculation is significantly reduced if the auxiliary degrees of freedom which purify the statistical operator are time evolved with the physical Hamiltonian but reversed time. We exploit this to investigate the long-time behavior of current correlation functions of the XXZ spin-1/2 Heisenberg chain. This allows a direct extraction of the Drude weight D at intermediate to large T. We find that D is nonzero--and thus transport is dissipationless--everywhere in the gapless phase. At low temperatures we establish an upper bound to D by comparing with bosonization.
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