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Simple Models of Non-Haldane Spin Liquid with Exact Ground States

Alexei K. Kolezhuk, H.-J. Mikeska

Published Dec 8, 1997• 0 citations
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Abstract

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.

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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 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 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.
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.
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 phase diagram of a frustrated S=1/2 antiferromagnetic spin ladder with additional next-nearest neighbor exchanges, both diagonal and inchain, is studied by a weak-coupling effective field theory approach combined with exact diagonalization for finite systems. In addition to two known phases with rung-singlet and Haldane-type ground states, we observe two new phases with dimerization along the chains. Furthermore, the transitions between the different phases are studied and shown to be either first order or to belong to the universality class of the two-dimensional Ising model. The nature of elementary excitations is discussed briefly.
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.