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arXiv:0712.3361 · Physical Review B

Dynamic probes of quantum spin chains with the Dzyaloshinskii-Moriya interaction

Oleg Derzhko, Taras Verkholyak, Taras Krokhmalskii, H. Büttner

Published Jun 6, 2006• 51 citations
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Abstract

We consider the spin-$\frac{1}{2}$ anisotropic $XY$ chain in a transverse $(z)$ field with the Dzyaloshinskii-Moriya interaction directed along the $z$ axis in spin space to examine the effect of the Dzyaloshinskii-Moriya interaction on the $zz$, $xx$, and $yy$ dynamic structure factors. Using the Jordan-Wigner fermionization approach we analytically calculate the dynamic transverse spin structure factor. It is governed by a two-fermion excitation continuum. We analyze the effect of the Dzyaloshinskii-Moriya interaction on the two-fermion excitation continuum. Other dynamic structure factors which are governed by many-fermion excitations are calculated numerically. We discuss how the Dzyaloshinskii-Moriya interaction manifests itself in the dynamic properties of the quantum spin chain at various fields and temperatures.

DOI
10.1103/physrevb.73.214407

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We consider the spin-12\frac{1}{2}21​ anisotropic XYXYXY chain in a transverse (z)(z)(z) field with the Dzyaloshinskii-Moriya interaction directed along the zzz axis in spin space to examine the effect of the Dzyaloshinskii-Moriya interaction on the zzzzzz, xxxxxx, and yyyyyy dynamic structure factors. Using the Jordan-Wigner fermionization approach we analytically calculate the dynamic transverse spin structure factor. It is governed by a two-fermion excitation continuum. We analyze the effect of the Dzyaloshinskii-Moriya interaction on the two-fermion excitation continuum. Other dynamic structure factors which are governed by many-fermion excitations are calculated numerically. We discuss how the Dzyaloshinskii-Moriya interaction manifests itself in the dynamic properties of the quantum spin chain at various fields and temperatures.
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.
We consider a spin-1/2 XX chain with three-spin interactions which is equivalent to a system of noninteracting spinless fermions.We examine some dynamic quantities of the spin model.In particular,we calculate analytically the dynamic transverse (zz) structure factor which is governed by a two-fermion excitation continuum.Moreover,we compute numerically the dynamic xx structure factor which is a many-fermion dynamic quantity.We illustrate how the three-spin interactions manifest themselves in the dynamic probes.
We consider a spin-12\frac{1}{2}21​ XYXYXY chain in a transverse (z)(z)(z) field with multisite interactions. The additional terms introduced into the Hamiltonian involve products of spin components related to three adjacent sites. A Jordan--Wigner transformation leads to a simple bilinear Fermi form for the resulting Hamiltonian and, hence, the spin model admits a rigorous analysis. We point out the close relationships between several variants of the model, which were discussed separately in previous studies. The ground-state phases (ferromagnet and two kinds of spin liquid) of the model are reflected in the dynamic structure factors of the spin chains, which are the main focus in this study. First, we consider the zzzzzz dynamic structure factor, reporting for this quantity a closed-form expression and analyzing the properties of the two-fermion (particle-hole) excitation continuum, which governs the dynamics of transverse spin component fluctuations and of some other local operator fluctuations. Then we examine the xxxxxx dynamic structure factor, which is governed by many-fermion excitations, reporting both analytical and numerical results. We discuss some easily recognized features of the dynamic structure factors, which are signatures of the presence of the three-site interactions.
The Jordan-Wigner transformation is known as a powerful tool in condensed matter theory, especially in the theory of low-dimensional quantum spin systems. The aim of this chapter is to review the application of the Jordan-Wigner fermionization technique for calculating dynamic quantities of low-dimensional quantum spin models. After a brief introduction of the Jordan-Wigner transformation for one-dimensional spin one-half systems and some of its extensions for higher dimensions and higher spin values we focus on the dynamic properties of several lowdimensional quantum spin models. We start from the famous s = 1/2 XX chain. As a first step we recall well-known results for dynamics of the z-spin-component fluctuation operator and then turn to the dynamics of the dimer and trimer fluctuation operators. The dynamics of the trimer fluctuations involves both the two-fermion (one particle and one hole) and the four-fermion (two particles and two holes) excitations. We discuss some properties of the two-fermion and four-fermion excitation continua. The four-fermion dynamic quantities are of intermediate complexity between simple two-fermion (like the zz dynamic structure factor) and enormously complex multi-fermion (like the xx or xy dynamic structure factors) dynamic quantities. Further we discuss the effects of dimerization, anisotropy of XY interaction, and additional Dzyaloshinskii-Moriya interaction on various dynamic quantities. Finally we consider the dynamic transverse spin structure factor Szz(k, ω) for the s = 1/2 XX model on a spatially anisotropic square lattice which allows one to trace a one-to-two-dimensional crossover in dynamic quantities.