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Journal of Physics Condensed Matter

On the energy spectrum of a spin lattice formed by a finite number of coupled spin-1/2XYchains

Vladyslav O. Cheranovskii, E. V. Ezerskaya, T O Kuznetsova

Published Aug 22, 2002• 0 citations
Publisher

Abstract

We studied the energy spectrum of a spin lattice formed by m XY spin-1/2 chains with Ising inter-chain coupling. For strong ferromagnetic coupling we found that the lowest-energy states for non-zero numbers of inverted spins on each XY chain have n-magnon bound character if n = ml − 1, where l = 2, 3,.... For a spin tube formed by three XY chains with strong ferromagnetic inter-chain coupling, the lowest-energy states are described by the XXZ spin-1/2 chain model with antiferromagnetic coupling.

DOI
10.1088/0953-8984/14/34/321

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We studied the energy spectrum of a spin lattice formed by m XY spin-1/2 chains with Ising inter-chain coupling. For strong ferromagnetic coupling we found that the lowest-energy states for non-zero numbers of inverted spins on each XY chain have n-magnon bound character if n = ml − 1, where l = 2, 3,.... For a spin tube formed by three XY chains with strong ferromagnetic inter-chain coupling, the lowest-energy states are described by the XXZ spin-1/2 chain model with antiferromagnetic coupling.
We studied the energy spectrum of two coupled XY spin-1/2 chains with different exchange integrals and inter-chain interaction of Ising type. The thorough analytical treatment of two-magnon states was given for finite and infinite lattice strips. To study the case of macroscopic number of inverted spins we used the corresponding density matrix renormalization group (DMRG) simulation. We also derived the self-consistent Bardeen-Cooper-Schrieffer (BCS) estimates for the lowest energies of the system. The comparison of the BCS and the DMRG estimates has shown incorrect behaviour of the BCS approximation for energy as a function of the intra-chain exchange integrals. To use the analytical results for two-magnon bound states we proposed a simple approximate formula for the lowest n -magnon energies of an infinite ladder with a more correct dependence on model parameters.
The location of the XY phase in the ground-state phase diagram of the spin-1/2 anisotropic ferromagnetic-antiferromagnetic alternating Heisenberg chain is determined. This model reduces to the spin-1 XXZ chain if the ferromagnetic bond is infinitely strong. The phase boundary between the XY phase and the Haldane phase is determined from the analysis of the numerically obtained energy spectrum of finite-sized systems with the open boundary condition. Our results are consistent with the series-expansion results by Yamanaka et al . within their error bars. The boundary between the ferromagnetic phase and the XY phase is also determined by comparing the energy eigenvalues of these two phases.
Abstract We studied the energy spectrum of the 1‐D extended Hubbard model with spin‐dependent hopping and related spin ladder system formed by two coupled XXZ spin 1/2 chains with the interchain interaction of Ising type. It was proved that the model excitation spectrum has no gap excepting some special values of z‐projection of the ground‐state total spin. The thorough analytic consideration of two‐magnon states was given. The existence up to five bound states at specified value of quasimomentum of the pair of inverted spins was shown. We also present the results of density matrix renormalization group calculations that showed nonadequacy of the pair approximation for n‐magnon bound states of the extended model with the strong electron–electron interactions. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002
The low energy behavior of the S=1/2 antiferromagnetic XY-like XXZ chains with precious mean quasiperiodic exchange modulation is studied by the density matrix renormalization group method. It is found that the energy gap of the chain with length N scales as exp⁡(−cNω)\exp (-cN^ω)exp(−cNω) with nonuniversal exponent ωωω if the Ising component of the exhange coupling is antiferromagnetic. This behavior is expected to be the characteristic feature of the quantum spin chains with relevant aperiodicity. This is in contrast to the XY chain for which the precious mean exchange modulation is marginal and the gap scales as N−zN^{-z}N−z. On the contrary, it is also verified that the energy gap scales as N−1N^{-1}N−1 if the Ising component of the exhange coupling is ferromagnetic. Our results are not only consistent with the recent bosonization analysis of Vidal, Mouhanna and Giamarchi but also clarify the nature of the strong coupling regime which is inaccesssible by the bosonization approach.
Results are presented and interpreted for the zero- and finite-temperature excitation spectrum of ferromagnetic Ising-Heisenberg chains, as probed by dynamic form factors. Finite-chain calculations demonstrate the occurrence of a thermally induced resonance centered around zero frequency, and a broadening of the magnon and two-magnon bound-state resonances at low TTT. The occurrence of bound states in the associated transitions demonstrates the failure of finite-order magnon perturbation theory.