Spin conductivity of the XXZ chain in the antiferromagnetic massive regime
We present a series representation for the dynamical two-point function of the local spin current for the XXZ chain in the antiferromagnetic massive regime at zero temperature. From this series we can compute the correlation function with very high accuracy up to very long times and large distances....
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Published in | SciPost physics Vol. 12; no. 5; p. 158 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
SciPost Foundation
01.05.2022
SciPost |
Subjects | |
Online Access | Get full text |
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Summary: | We present a series representation for the dynamical two-point
function of the local spin current for the XXZ chain in the
antiferromagnetic massive regime at zero temperature. From this
series we can compute the correlation function with very high
accuracy up to very long times and large distances. Each term in
the series corresponds to the contribution of all scattering
states of an even number of excitations. These excitations can
be interpreted in terms of an equal number of particles and holes.
The lowest term in the series comprises all scattering states
of one hole and one particle. This term determines the long-time
large-distance asymptotic behaviour which can be obtained
explicitly from a saddle-point analysis. The space-time
Fourier transform of the two-point function of currents
at zero momentum gives the optical spin conductivity of
the model. We obtain highly accurate numerical estimates for
this quantity by numerically Fourier transforming our data.
For the one-particle, one-hole contribution, equivalently
interpreted as a two-spinon contribution, we obtain an exact
and explicit expression in terms of known special functions.
For large enough anisotropy, the two-spinon contribution carries
most of the spectral weight, as can be seen by calculating
the f-sum rule. |
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ISSN: | 2542-4653 2542-4653 |
DOI: | 10.21468/SciPostPhys.12.5.158 |