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arXiv:cond-mat/9604068 · Journal of Physics Condensed Matter

The - antiferromagnet on the square lattice with Dzyaloshinskii - Moriya interaction: an exact diagonalization study

Andreas Voigt, Johannes Richter

Published Jul 1, 1996• 4 citations
arXivHTMLPDF

Abstract

We examine the influence of an anisotropic interaction term of Dzyaloshinskii - Moriya (DM) type on the ground state ordering of the - spin- Heisenberg antiferromagnet on the square lattice. For the DM term we consider several symmetries corresponding to different crystal structures. For the pure - model there are strong indications for a quantum spin liquid in the region of . We find that a DM interaction influences the breakdown of the conventional antiferromagnetic order by (i) shifting the spin-liquid region, (ii) changing the isotropic character of the ground state towards anisotropic correlations and (iii) creating for certain symmetries a net ferromagnetic moment.

DOI
10.1088/0953-8984/8/27/015

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We examine the influence of an anisotropic interaction term of Dzyaloshinskii - Moriya (DM) type on the ground state ordering of the - spin- Heisenberg antiferromagnet on the square lattice. For the DM term we consider several symmetries corresponding to different crystal structures. For the pure - model there are strong indications for a quantum spin liquid in the region of . We find that a DM interaction influences the breakdown of the conventional antiferromagnetic order by (i) shifting the spin-liquid region, (ii) changing the isotropic character of the ground state towards anisotropic correlations and (iii) creating for certain symmetries a net ferromagnetic moment.
A preponderance of evidence suggests that the ground state of the nearest-neighbor S=1/2S=1/2S=1/2 antiferromagnetic Heisenberg model on the kagome lattice is a gapless spin liquid. Many candidate materials for the realization of this model possess in addition a Dzyaloshinskii-Moriya (DM) interaction. We study this system by tensor-network methods and deduce that a weak but finite DM interaction is required to destabilize the gapless spin-liquid state. The critical magnitude, ${D}_{c}/J\ensuremath{\simeq}0.012(2)$, lies well below the DM strength proposed in the kagome material herbertsmithite, indicating a need to reassess the apparent spin-liquid behavior reported in this system.
We study the effects of the Dzyaloshinski-Moriya (DM) anisotropic interaction on the ground-state properties of the Heisenberg XY spin chain by means of the fidelity susceptibility, order parameter, and entanglement entropy. Our results show that the DM interaction could influence the distribution of the regions of quantum phase transitions and cause different critical regions in the XY spin model. Meanwhile, the DM interaction has effective influence on the degree of entanglement of the system and could be used to increase the entanglement of the spin system.
Motivated by the recent neutron-scattering experiment on Rb2{}_{2}2​Cu3{}_{3}3​SnF12{}_{12}12​ [Nature Phys. 6, 865 (2010)], we investigate the effect of Dzyaloshinskii-Moriya interactions in a theoretical model for the magnetic structure of this material. Considering the valence bond solid ground state, which has a 12-site unit cell, we develop the bond operator mean-field theory. It is shown that the Dzyaloshinskii-Moriya interactions significantly modify the triplon dispersions around the $\ensuremath{\Gamma}$ point and cause a shift of the spin-gap (the minimum triplon gap) position from the KKK to $\ensuremath{\Gamma}$ point in the first Brillouin zone. The spin gap is also evaluated in exact diagonalization studies on a 24-site cluster. We discuss a magnetic transition induced by the Dzyaloshinskii-Moriya interactions in the bond operator framework. Moreover, the magnetization process under external magnetic fields is studied within the exact diagonalization approach. We find that the results of both approaches are consistent with the experimental findings.
In the present paper, an influence of the anisotropic antisymmetric exchange interaction, the Dzialoshinskii–Moriya (DM) interaction, on entanglement of two qubits in various magnetic spin models, including the pure DM model and the most general XYZ model, are studied. We find that the time evolution generated by DM interaction can implement the SWAP gate and discuss realistic quasi-one-dimensional magnets where it can be realized. It is shown that inclusion of the DM interaction to any Heisenberg model creates, when it does not exist, or strengthens, when it exists, the entanglement. We give physical explanation of these results by studying the ground state of the systems at T = 0. Nonanalytic dependence of the concurrence on the DM interaction and its relation with quantum phase transition is indicated. Our results show that spin models with the DM coupling have some potential applications in quantum computations and the DM interaction could be an efficient control parameter of entanglement.