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arXiv:cond-mat/9710114 · Journal of Physics Condensed Matter

Elementary excitations in the gapped phase of a frustratedS= 1/2 spin ladder: from spinons to the Haldane triplet

S. Brehmer, Alexei K. Kolezhuk, H.-J. Mikeska, U Neugebauer

Published Feb 9, 1998• 20 citations
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Abstract

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.

DOI
10.1088/0953-8984/10/5/017

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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.
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.
The phase diagram of a frustrated S=1∕2S=1∕2S=1∕2 antiferromagnetic spin ladder with additional next-nearest neighbor exchanges, both diagonal and in-chain, 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.
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 investigate the phase diagram of antiferromagnetic spin ladders with additional exchange interactions on diagonal bonds by variational and numerical methods. These generalized spin ladders interpolate smoothly between the [Formula: see text] chain with competing nn and nnn interactions, the [Formula: see text] chain with alternating exchange and the antiferromagnetic (AF) S = 1 chain. The Majumdar - Ghosh ground states are formulated as matrix product states and are shown to exhibit the same type of hidden order as the AF S = 1 chain. Generalized matrix product states are used for a variational calculation of the ground state energy and the spin and string correlation functions. Numerical (Lanczos) calculations of the energies of the ground state and of the low-lying excited states are performed, and compare reasonably with the variational approach. Our results support the hypothesis that the dimer and Majumdar - Ghosh points are in the same phase as the AF S = 1 chain.
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 have obtained an analytic expression for the k-dependence of the excitation energy gap for an arbitrary double S = 1/2 spin chain by using the non-local unitary transformation and the variational method. We check that it explains the gap behaviour of various systems, which include the Haldane system and the dimer system in both extreme limits, and also the ladder model and the Majumdar - Ghosh model. The string order parameter, the dimer order parameter, and the local spin value are also calculated in the ground state. The ground-state energy exhibits a great stabilization by an antiferromagnetic bond dimerization, which might be realized in various new compounds. We also mention the relation of the convergence to the Haldane state with the spin-exchange symmetry of the model. The excited state has one domain wall of a local triplet type except in the vicinity of the Majumdar - Ghosh point, where a local triplet is decomposed into two S = 1/2 free spins moving among the singlet dimers.