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arXiv:cond-mat/0008321 · Physical review. B, Condensed matter

Elementary excitations in one-dimensional spin-orbit models: Neutral and charged solitons and their bound states

Alexei K. Kolezhuk, H.-J. Mikeska, U. Schollwöck

Published Jan 22, 2001• 20 citations
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Abstract

We study, both numerically and variationally, the interplay between different types of elementary excitations in the model of a spin chain with anisotropic spin-orbit coupling, in the vicinity of the ``dimer line'' with an exactly known dimerized ground state. Our variational treatment is found to be in a qualitative agreement with the exact diagonalization results. Soliton pairs are shown to be the lowest excitations only in a very narrow region of the phase diagram near the dimer line, and the phase transitions are always governed by magnon-type excitations which can be viewed as soliton-antisoliton bound states. It is shown that when the anisotropy exceeds certain critical value, an additional phase boundary appears. In the doped model on the dimer line, the exact elementary charge excitation is shown to be a hole bound to a soliton. Bound states of those ``charged solitons'' are studied; exact solutions for N-hole bound states are presented.

DOI
10.1103/physrevb.63.064418

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We study, both numerically and variationally, the interplay between different types of elementary excitations in the model of a spin chain with anisotropic spin-orbit coupling, in the vicinity of the dimer line'' with an exactly known dimerized ground state. Our variational treatment is found to be in a qualitative agreement with the exact diagonalization results. Soliton pairs are shown to be the lowest excitations only in a very narrow region of the phase diagram near the dimer line, and the phase transitions are always governed by magnon-type excitations which can be viewed as soliton-antisoliton bound states. It is shown that when the anisotropy exceeds certain critical value, an additional phase boundary appears. In the doped model on the dimer line, the exact elementary charge excitation is shown to be a hole bound to a soliton. Bound states of those charged solitons'' are studied; exact solutions for N-hole bound states are presented.
The low-energy excitations and dynamics of a spin-orbital chain are calculated within a variational framework based on dimer states, exact diagonalization and the dynamical Density Matrix Renormalization Group (DMRG). In its dimerized phase, the spin-orbital chain exhibits a rich interplay of solitonic and magnonic excitations. While a solitonic excitation is the lowest excitation in a narrow region around the exactly solvable dimer point, magnonic excitations govern the phase transitions to neighbouring phases. Numerical calculations confirm that the curvature of the magnonic excitations is exactly flat on the so-called dimer line, changing sign across the line. This statement is not true for the solitonic excitations, which determine the lower edge of the excitation spectrum in the vicinity of the dimer line. DMRG calculations suggest that low-lying solitonic excitations may be experimentally hard to observe, with most spectral weight in higher-lying magnons.
We use the variational matrix-product ansatz to study elementary excitations in the ladder with additional diagonal coupling, equivalent to a single chain with alternating exchange and next-nearest-neighbour interaction. In the absence of alternation, the elementary excitation consists of two free particles (`spinons') which are solitons in the dimer order. When the nearest-neighbour exchange alternates, the `spinons' are confined into one S = 1 excitation which is a soliton in the generalized string order. The variational results are found to be in qualitative agreement with the exact-diagonalization data for 24 spins. We argue that such an approach gives a reasonably good description over a wide range of the model parameters.
We present a family of spin ladder models which admit exact solution for the ground state and exhibit non-Haldane spin liquid properties as predicted recently by Nersesyan and Tsvelik [Phys. Rev. Lett. v.78, 3939 (1997)], and study their excitation spectrum using a simple variational ansatz. The elementary excitation is neither a magnon nor a spinon, but a pair of propagating triplet or singlet solitons connecting two spontaneously dimerized ground states. Second-order phase transitions separate this phase from the Haldane phase and the rung-dimer phase.
Elementary excitations are studied near the Ising limit close to the degenerate point in the one-dimensional anisotropic Heisenberg antiferromagnets with up to next-nearest-neighbor interactions. Solitons in the Néel and (2,2) antiphase states and triplet-dimer excitations in the dimer state are found as propagating modes. These excitations are found to dominate the shape of the central peak in dynamical spin correlation functions, through the comparison with the numerical results by an exact diagonalization method for finite chains. The temperature dependence of the static correlation function is also discussed, and the shape is found to change gradually with increasing temperature, approaching the zero-temperature correlation function at the degenerate point.
A bond operator representation for three S=12S=\frac{1}{2}S=21​ spins is obtained along the same line as the two-spin cases. With the spin and the chirality freedom expressed by the same bond operators, we studied the elementary excitations of the spin-tube and the spin-orbit models. For 333-leg spin ladders and general spin ladders with an odd number of legs and periodic boundary conditions in the rung direction, the spinonlike excitations, which carry 12\frac{1}{2}21​ spin and chirality freedoms, are calculated by a variational ansatz. The magnonlike excitations, which denote the change of a dimerized bond from spin singlet to spin triplet and/or from chirality triplet to chirality singlet, or from one kind of chirality triplet to another chirality triplet, with different z-component, are also studied. Bound states of spinonlike excitation pairs exist near the vicinity of momentum zone center $\ensuremath{\pi}/2.$ The bond operators are also applied to other general spin-orbit models with spontaneously dimerized ground states, and the elementary excitations are studied.
The role of the spin-phonon coupling in spin-Peierls chains doped with spin-0 or spin-1 impurities is investigated by various numerical methods such as exact diagonalization, quantum Monte Carlo simulations and Density Matrix Renormalization Group. Various treatments of the lattice, in a fully quantum mechanical way, classically in the adiabatic approximation or using a fixed three-dimensional dimerization pattern are compared. For an isolated chain, strong bonds form between the two spin-1/2 sites next to the impurity site, leading to the appearance of magneto-elastic solitons. We also show that these excitations do not bind to spin-0 impurities but are weakly attracted by spin-1 impurities. However, the interchain elastic coupling generates an effective confining potential at the non-magnetic impurity site which can lead to the formation of soliton-impurity bound states. We also predict that a soliton and an antisoliton bound to two impurities on the same chain can annihilate each other when the separation between the impurities is smaller than a critical value depending on the interchain elastic constant.