Spin-Peierls instability in a quantum spin chain with Dzyaloshinskii-Moriya interaction

Abstract

We analysed the ground state energy of some dimerized spin-1 2 transverse XX and Heisenberg chains with Dzyaloshinskii-Moriya (DM) interaction to study the influence of the latter interaction on the spinPeierls instability. We found that DM interaction may act either in favour of the dimerization or against it. The actual result depends on the dependence of DM interaction on the distortion amplitude in comparison with such dependence for the isotropic exchange interaction.

Exact description of magnetoelectric effect in the spin-12XXZ chain with Dzyaloshinskii-Moriya interaction

“…40 The XX chain with the DM term is also exactly solvable within this context. [41][42][43][44] Thus, starting with the Hamiltonian (2.1) with = 0 and performing a Jordan-Wigner transformation to free fermions, …”

Density of states and phase diagram of the antiferromagnetic spin chain with Dzyaloshinsky–Moriya interaction and spin-phonon coupling

“…The threshold value b c can be obtained by letting the variation qm p =qD ¼ 0 ðDa0Þ; and in the nonadiabatic case, b c is determined by a set of values of D; l and o p . If b c was simply a constant as previous works predicted [21], lm p would not change with D when b ¼ b c . However, in view of the determination of m p by D, b, l and o p , one might wonder why the DM interaction should have no effect on dimerization when b ¼ b c .…”

“…The antisymmetric character of DM interaction is expressed by two principal cases, the uniform [18,19] and the staggered DM interactions [17,19,20], and has been studied by many previous authors. A numerical calculations of the groundstate energy of the spin-Peierls XX model and Heisenberg chain with DM interaction by Derzhko et al [21] found that uniform DM interaction may act against the dimerization but staggered DM interaction may act in favor of the dimerization. However, whether the staggered DM interaction always enhances the dimerization or the uniform DM interaction always acts against the dimerization has not been clearly answered.…”

“…Up to now, all of the theoretical studies on DM interaction in spin-chain systems have used the static model and treated the problem in adiabatic limit. By considering the static model, several attempts have been performed to treat the spin-phonon coupling [21,22]. The validity of this static model is based on the assumption that the frequencies of the phonons associated with the dimerization are much smaller than the dimerization gap and the exchange integral.…”

“…We start from the antiferromagnetic Heisenberg model with DM interaction and spin-phonon coupling [17,21,27] …”