arXiv:2011.00326

Low-temperature asymptotics for the transverse dynamical structure factor for a magnetically polarized $XX$ chain at small and negative frequencies

P. N. Bibikov

Published Oct 31, 2020• 0 citations

Abstract

Using the truncated form factor expansion the low-temperature asymptotics for the transverse dynamical structure factor of the magnetically polarized $XX$ chain is studied. Unlike the previous paper we do not use the representation of structure factor in terms of the corresponding magnetic susceptibility. This enables to obtain correct results at small and negative frequencies.

DOI: 10.48550/arxiv.2011.00326

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arXiv:2011.00326

Low-temperature asymptotics for the transverse dynamical structure factor for a magnetically polarized $XX$ chain at small and negative frequenciesLow-temperature asymptotics for the transverse dynamical structure factor for a magnetically polarized $XX$ chain at small and negative frequencies

P. N. Bibikov

Published Oct 31, 2020• 0 citations

arXiv HTML PDF

Abstract

Using the truncated form factor expansion the low-temperature asymptotics for the transverse dynamical structure factor of the magnetically polarized

XX

chain is studied. Unlike the previous paper we do not use the representation of structure factor in terms of the corresponding magnetic susceptibility. This enables to obtain correct results at small and negative frequencies.

DOI: 10.48550/arxiv.2011.00326

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P N Bibikov

Abstract The Dyson equation for the real two-time commutator retarded one-magnon Green function of the ferromagnetically polarized XX chain is suggested following the Plakida–Tserkovnikov algorithm. Starting from this result a low-temperature integral representation for the corresponding magnon self-energy is obtained by the truncated form factor expansion, however, without any resummations. Within the suggested approach, the low-temperature asymptotics of the transverse dynamical structure factor may be readily studied. Some obtained line shapes are presented.Abstract The Dyson equation for the real two-time commutator retarded one-magnon Green function of the ferromagnetically polarized XX chain is suggested following the Plakida–Tserkovnikov algorithm. Starting from this result a low-temperature integral representation for the corresponding magnon self-energy is obtained by the truncated form factor expansion, however, without any resummations. Within the suggested approach, the low-temperature asymptotics of the transverse dynamical structure factor may be readily studied. Some obtained line shapes are presented.

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The ferromagnetically polarized gapped XXZ spin chain is studied at low temperatures. Utilizing only the one- and two-magnon spectrums and focusing on the magnon-creation contribution to the transverse dynamical susceptibility, we represent the latter in the form of the Dyson equation. Then, following the well known correspondence between the imaginary part of magnetic susceptibility and dynamical structure factor, we get the low-temperature formula for the magnon-peak lineshape. The suggested approach is effective only if the processes related to magnon creations and to transitions from magnons to coupled magnon pairs are energetically separated. As it is shown in the paper, such separation is inherent in the easy-axis chains with rather strong anisotropy. We present several plots and discuss their lineshapes. As the supplemental result we obtain integral representations for the temperature-dependent magnon resonance shift and the parameter which is usually associated with the decay rate. The low-temperature behavior of the resonance shift is studied in details. All calculations are performed up to controllable error $o({e}^{\ensuremath{-}\ensuremath{\beta}{E}_{\mathrm{gap}}})$.The ferromagnetically polarized gapped XXZ spin chain is studied at low temperatures. Utilizing only the one- and two-magnon spectrums and focusing on the magnon-creation contribution to the transverse dynamical susceptibility, we represent the latter in the form of the Dyson equation. Then, following the well known correspondence between the imaginary part of magnetic susceptibility and dynamical structure factor, we get the low-temperature formula for the magnon-peak lineshape. The suggested approach is effective only if the processes related to magnon creations and to transitions from magnons to coupled magnon pairs are energetically separated. As it is shown in the paper, such separation is inherent in the easy-axis chains with rather strong anisotropy. We present several plots and discuss their lineshapes. As the supplemental result we obtain integral representations for the temperature-dependent magnon resonance shift and the parameter which is usually associated with the decay rate. The low-temperature behavior of the resonance shift is studied in details. All calculations are performed up to controllable error $o({e}^{\ensuremath{-}\ensuremath{\beta}{E}_{\mathrm{gap}}})$.

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arXiv:cond-mat/9701052Physical review. B, Condensed matterJun 1, 199766 citations

Low-temperature asymptotics for the transverse dynamical structure factor for a magnetically polarized

XX

chain at small and negative frequencies

Using the truncated form factor expansion the low-temperature asymptotics for the transverse dynamical structure factor of the magnetically polarized

XX

Magnon peak lineshape in the transverse dynamical structure factor of a magnetically polarized easy-axis

XXZ

chain at low temperatures

o({\rm e}^{-βE_{gap}})

{\mathrm{T}}_{1}

from the \ensuremath{\omega}\ensuremath{\rightarrow}0 limit, and compare with recent experimental results for

{\mathrm{Sr}}_{2}

{\mathrm{CuO}}_{3}

and

{\mathrm{CuGeO}}_{3}

. We also discuss the scaling behavior of the dynamic susceptibility, and of the static structure factor S(k) and the static susceptibility \ensuremath{\chi}(k). We confirm the asymptotic low-temperature forms S(\ensuremath{\pi})\ensuremath{\sim}[ln (T)

{]}^{3\mathrm{/}2}

and \ensuremath{\chi}(\ensuremath{\pi})\ensuremath{\sim}${\mathrm{T}}^{\mathrm{\ensuremath{-}}1}$[ln (T)

{]}^{1\mathrm{/}2}

, expected from previous theoretical studies.