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arXiv:2001.04159 · Physical review. B./Physical review. B

Spin- 12 XX chain in a transverse field with regularly alternating g factors: Static and dynamic properties

Taras Krokhmalskii, Taras Verkholyak, O. R. Baran, Vadim Ohanyan, Oleg Derzhko

Published Oct 2, 2020• 4 citations
arXivHTMLPDF

Abstract

We consider the spin-$\frac{1}{2}$ isotropic XY chain in an external magnetic field directed along the $z$ axis with periodically varying $g$ factors. To reveal the effects of regularly alternating $g$ factors, we calculate various static and dynamic equilibrium quantities in the ground state and at finite temperatures. We demonstrate that because of the regularly alternating $g$ factors the saturation field may disappear and the field dependence of the susceptibility in the ground state has additional logarithmic singularity at zero field. Moreover, the zero-field susceptibility has a logarithmic singularity as $T\ensuremath{\rightarrow}0$. Furthermore, the dynamic structure factors exhibit much more structure in the ``wave vector--frequency'' plane that can be traced out to modifications of the two-fermion excitation continua which exclusively determine ${S}_{zz}(\ensuremath{\kappa},\ensuremath{\omega})$ and dominate the properties of ${S}_{xx}(\ensuremath{\kappa},\ensuremath{\omega})$. We discuss what changes can be observed in dynamic experiments on the corresponding substances.

DOI
10.1103/physrevb.102.144403

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Using continued fractions we study the ground state properties of the spin-½ Ising chain in a transverse field with periodically varying interaction strengths and external fields. We consider in detail the chain having a period-2 modulation of the interaction strengths and compare the results obtained with those corresponding to the spin-½ isotropic XY chain in a transverse field. In contrast to the behaviour of the transverse XY chain, the transverse Ising chain does not exhibit a step-like magnetization versus field dependence caused by the alternation of bonds. Its susceptibility exhibits a logarithmic singularity at a field determined by interaction strengths, and it is stable with respect to spin-Peierls dimerization.
We have considered a numerical scheme for the calculation of the equilibrium properties of spin-1/2 XY chains. Within its frames it is necessary to solve in the last resort only the 2N\times 2N eigenvalue and eigenvector problem but not the 2^N\times 2^N one as for an arbitrary system consisting of N spins 1/2. To illustrate the approach we have presented some new results. Namely, the xx dynamic structure factor for the Ising model in transverse field, the density of states for the isotropic chain with random intersite couplings and transverse fields that linearly depend on the surrounding couplings, and the zz dynamic structure factor for the Ising model in random transverse field. The results obtained are hopped to be useful for an interpretation of observable data for one-dimensional spin-1/2 XY substances.
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The zz and xx ( yy ) dynamic structure factors of the dimerized spin-½ isotropic XY chain in a transverse ( z ) field are calculated for arbitrary temperatures. The zz structure factor can be given in analytical terms, involving a single integration, whereas the xx dynamic structure factor can be evaluated completely numerically for very long chains. We compare the two structure factors and discuss in some detail how a dimerization manifests itself in the dynamic structure factors at different external fields and temperatures. We compare our results to corresponding results for the dimerized Heisenberg chain obtained by approximate techniques.
Dynamic xx and xy spin pair correlation functions for the isotropic spin-½ XY chain are calculated numerically for long open chains in the presence of a transverse ( z ) magnetic field at finite temperature. From these data the first numerical results for the dynamic structure factors S xx (κ,ω) and S xy (κ,ω) are obtained and compared with the known results for S zz (κ,ω). While S zz (κ,ω) is restricted to certain regions in the (κ,ω)-plane S xx (κ,ω) and S xy (κ,ω) are not. Nevertheless, the numerical results show that the latter structure factors are quite small outside the regions defined by S zz (κ,ω) and moreover, that they may in many circumstances, especially at low temperature, be approximately described by a small number of broadened excitation branches.