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arXiv:1801.10572 · Physical review. B./Physical review. B

Finite-temperature dynamic structure factor of the spin-1 XXZ chain with single-ion anisotropy

Florian Lange, Satoshi Ejima, Holger Fehske

Published Feb 12, 2018• 20 citations
arXivHTMLPDF

Abstract

Improving matrix-product state techniques based on the purification of the density matrix, we are able to accurately calculate the finite-temperature dynamic response of the infinite spin-1 $\text{XXZ}$ chain with single-ion anisotropy in the Haldane, large-$D$, and antiferromagnetic phases. Distinct thermally activated scattering processes make a significant contribution to the spectral weight in all cases. In the Haldane phase, intraband magnon scattering is prominent, and the on-site anisotropy causes the magnon to split into singlet and doublet branches. In the large-$D$ phase response, the intraband signal is separated from an exciton-antiexciton continuum. In the antiferromagnetic phase, holons are the lowest-lying excitations, with a gap that closes at the transition to the Haldane state. At finite temperatures, scattering between domain-wall excitations becomes especially important and strongly enhances the spectral weight for momentum transfer $\ensuremath{\pi}$.

DOI
10.1103/physrevb.97.060403

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Improving matrix-product state techniques based on the purification of the density matrix, we are able to accurately calculate the finite-temperature dynamic response of the infinite spin-1 XXZ\text{XXZ}XXZ chain with single-ion anisotropy in the Haldane, large-DDD, and antiferromagnetic phases. Distinct thermally activated scattering processes make a significant contribution to the spectral weight in all cases. In the Haldane phase, intraband magnon scattering is prominent, and the on-site anisotropy causes the magnon to split into singlet and doublet branches. In the large-DDD phase response, the intraband signal is separated from an exciton-antiexciton continuum. In the antiferromagnetic phase, holons are the lowest-lying excitations, with a gap that closes at the transition to the Haldane state. At finite temperatures, scattering between domain-wall excitations becomes especially important and strongly enhances the spectral weight for momentum transfer \ensuremathπ\ensuremath{\pi}\ensuremathπ.
The antiferromagnetic spin-one chain is considerably one of the most fundamental quantum many-body systems, with symmetry-protected topological order in the ground state. Here, we present results for its dynamical spin structure factor at finite temperatures, based on a combination of exact numerical diagonalization, matrix-product-state calculations, and quantum Monte Carlo simulations. Open finite chains exhibit a subgap band in the thermal spectral functions, indicative of localized edge states. Moreover, we observe the thermal activation of a distinct low-energy continuum contribution to the spin spectral function with an enhanced spectral weight at low momenta and its upper threshold. This emerging thermal spectral feature of the Haldane spin-one chain is shown to result from intraband magnon scattering due to the thermal population of the single-magnon branch, which features a large bandwidth-to-gap ratio. These findings are discussed with respect to possible future studies on spin-one chain compounds based on inelastic neutron scattering.
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The spin-12\frac{1}{2}21​ XXZ chain with easy-plane anisotropy in a transverse field describes well the thermodynamic properties of the material Cs2CoCl4{\mathrm{Cs}}_{2}{\mathrm{CoCl}}_{4}Cs2​CoCl4​ in a wide range of temperatures and fields including the region close to the spin-flop Ising quantum phase transition. For a comparison with prospective inelastic neutron scattering experiments on this compound, we present results of an extensive numerical study of its dynamic structure factor ${\mathcal{S}}^{\ensuremath{\alpha}\ensuremath{\beta}}(k,\ensuremath{\omega})$ using matrix-product-state (MPS) techniques. Close to criticality, the dynamic part of the correlator Sxx{\mathcal{S}}^{xx}Sxx longitudinal to the applied field is incoherent and possesses a small total weight as the ground state is already close to saturation. The transverse correlator Szz{\mathcal{S}}^{zz}Szz, on the other hand, is dominated by a coherent single-particle excitation with additional spectral weight at higher energies that we tentatively attribute to a repulsively bound pair of particles. With increasing temperature, the latter quickly fades and spectral weight instead accumulates close to zero wave vector just above the single-particle energy. On a technical level, we compare the numerical efficiency of real-time evolution to an MPS-based Chebyshev expansion in the present context, finding that both methods yield results of similar quality at comparable numerical costs.
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