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Dzyaloshinski-Moriya interaction in S=½ ladder

E. Orignac, R. Citro

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

Using a Majorana fermion representation, we discuss the influence of Dzyaloshinski--Moriya interaction on the magnetic properties of a spin-1/2 ladder. We calculate the spin-echo decay rate and analyze the modifications with respect to the isotropic ladder. Implications of our calculations for experiments on ladder systems are discussed.

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arXiv:0712.2507•Journal of the Physical Society of Japan•Oct 10, 2006•8 citations
We investigate the effects of the Dzialoshinskii-Moriya (DM) and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interactions on various thermodynamic and magnetic properties of a spin-1/2 ladder. Using the Majorana fermion representation, we derive the spectrum of low energy excitations for a pure DM interaction and in presence of a superimposed KSEA interaction. We calculate the various correlation functions for both cases and discuss how they are modified with respect to the case of an isotropic ladder. We also discuss the electron spin resonance (ESR) spectrum of the system and show that it is strongly influenced by the orientation of the magnetic field with respect to the Dzialoshinskii-Moriya vector. Implications of our calculations for nuclear magnetic resonance and ESR experiments on ladder systems are discussed.
The spin ladder with Dzyaloshinsky—Moriya interaction is investigated by using the quantum renormalization-group method. The entanglement and fidelity are periodic functions of the time and oscillate between zero and one. The oscillation period decreases with either the interaction in the spin ladder or the Dzyaloshinsky—Moriya interaction increasing. When the system relates to the environment, both entanglement and fidelity oscillate with a damping rate related to intrinsic decoherence rate, the interaction in the spin ladder, and the Dzyaloshinsky—Moriya interaction.
By introducing the Dzyaloshinsky-Moriya (DM) interaction, the Loschmidt Echo ( LE ) of a quantum system consisting of a central spin and its surrounding environment characterized by an XY spin chain was investigated analytically and numerically. At the critical points of the magnetic field, the LE presents an obvious decay. The decay amplitude can be tuned by the DM interaction. In some specific intervals the DM interaction can remarkably delay the decay of the LE . On the other hand, the DM interaction can change the effects of the anisotropy parameter on the LE.
By introducing the Dzyaloshinsky–Moriya (DM) interaction, the Loschmidt Echo (LE) of a quantum system consisting of a central spin and its surrounding environment characterized by an XY spin chain was investigated. The analytical expression of the LE was obtained. The effects of magnetic field, DM interaction, spin chain size, and anisotropy parameter on the evolution behavior of the LE were discussed numerically. At the critical points of magnetic field, the LE presents an obvious decay following with local oscillation. The decaying and oscillation behavior of the LE can be tuned by the intensity of the DM interaction. With increasing the spin chain size, the decaying amplitude is increased and the following oscillation behavior vanishes for the spin chain with larger size. The effect of the anisotropy parameter on the LE presents different properties at both sides of the knee point. The effect of the DM interaction on the decay of the LE is also related to the value of anisotropy parameter.
The temperature dependence of the static spin susceptibility, χ, and NMR relaxation rate, T 1 -1 , of S =1/2 Heisenberg two-leg ladder systems have been studied based on the Majorana fermion representation of the S =1/2 Heisenberg spin Hamiltonian introduced by Shelton, Nersesyan and Tsvelik (Phys. Rev. B 53 (1996) 8521). It is shown that in the case of SrCu 2 O 3 , we can fit the experimental data of χ and T 1 -1 in terms of the massive Majorana fermion excitation with mass m =440 K to resolve the apparent discrepancy of the spin gap activation energies between χ and T 1 -1 .
We consider the spin-1/2 isotropic XY chain in a (z) transverse magnetic field with the Dzyaloshinskii-Moriya interaction directed along the z-axis in spin space and examine the effects of the latter interaction on the zz, xx (yy) and xy (yx) dynamic structure factors. The Dzyaloshinskii-Moriya interaction does not manifest itself in the zz dynamic quantities. In contrast, the xx (yy) and xy (yx) dynamic structure factors show dramatical changes owing to the Dzyaloshinskii-Moriya interaction. Implications of our results for electron spin resonance experiments are briefly discussed.