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arXiv:cond-mat/9712087 · Physical Review Letters

Non-Haldane Spin-Liquid Models with Exact Ground States

Alexei K. Kolezhuk, H.-J. Mikeska

Published Mar 23, 1998• 111 citations
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Abstract

We present a family of spin-ladder models which can be solved exactly for the ground state and exhibit non-Haldane spin-liquid properties as predicted recently by Nersesyan and Tsvelik [Phys. Rev. Lett. 78, 3939 (1997)], and study their excitation spectra 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.

DOI
10.1103/physrevlett.80.2709

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We present a family of spin-ladder models which can be solved exactly for the ground state and exhibit non-Haldane spin-liquid properties as predicted recently by Nersesyan and Tsvelik [Phys. Rev. Lett. 78, 3939 (1997)], and study their excitation spectra 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.
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.
We study two-leg S=1/2 ladders with general isotropic exchange interactions between spins on neighboring rungs, whose ground state can be found exactly in a form of finitely correlated (matrix product) wave function. Two families of models admitting an exact solution are found: one yields translationally invariant ground states and the other describes spontaneously dimerized models with twofold degenerate ground state. Several known models with exact ground states (Majumdar–Ghosh and Shastry–Sutherland spin-1/2 chains, Affleck–Kennedy–Lieb–Tasaki spin-1 chain, Δ-chain, Bose–Gayen ladder model) can be obtained as particular cases from the general solution of the first family, which includes also a set of models with only bilinear interactions. Those two families of models have nonzero intersection, which enables us to determine exactly the phase boundary of the second-order transition into the dimerized phase and to study the properties of this transition. The structure of elementary excitations in the dimerized phase is discussed on the basis of a variational ansatz. For a particular class of models, we present exact wave functions of the elementary excitations becoming gapless at second-order transition lines. We also propose a generalization of the Bose–Gayen model which has a rich phase diagram with all phase boundaries being exact.
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.
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.
It is shown that a sufficiently strong four-spin interaction in the spin-1/2 spin ladder can cause dimerization. Such interaction can be generated either by phonons or (in the doped state) by the conventional Coulomb repulsion between the holes. The dimerized phases are thermodynamically undistinguishable from the Haldane phase, but have dramatically different correlation functions: the dynamical magnetic susceptibility, instead of displaying a sharp single magnon peak near $q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\pi}$, shows only a two-particle threshold separated from the ground state by a gap.
Motivated by the rich phase diagrams recently unveiled in frustrated spin-1 chains with competing next-nearest-neighbor and four-spin interactions, we investigate the nature of the elementary excitations of spin-1 chains in the vicinity of phase transitions using the matrix-product state (MPS) representation of elementary excitations. First, we show that both spinons and magnons naturally arise in SU(2)\mathrm{SU}(2)SU(2) invariant spin chains when describing ground states and elementary excitations using MPSs. Then we investigate the nature of the elementary excitations across the first-order transition between the Haldane phase and the topologically trivial next-nearest-neighbor Haldane phase. We show explicitly that spinons deconfine at the transition, and we calculate the dispersion of these deconfined spinons with MPSs. We also show that, immediately away from the transition line, spinons confine, forming dispersive spinon/antispinon bound states on both sides of the transition. Finally, we show that deconfined spinons also appear at the transition between the Haldane phase and the spontaneously dimerized phase when this transition is first order.