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Physical review. E

Sublattice entanglement in an exactly solvable anyonlike spin ladder

Balázs Pozsgay, Arthur Hutsalyuk, Levente Pristyák, G. Takács

Published Oct 14, 2022• 8 citations
Publisher

Abstract

We introduce an integrable spin ladder model and study its exact solution, correlation functions, and entanglement properties. The model supports two particle types (corresponding to the even and odd sublattices), such that the scattering phases are constants: Particles of the same type scatter as free fermions, whereas the interparticle phase shift is a constant tuned by an interaction parameter. Therefore, the spin ladder bears similarities with anyonic models. We present exact results for the spectrum and correlation functions, and we study the sublattice entanglement by numerical means.

DOI
10.1103/physreve.106.044120

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We present an integrable spin ladder model which possesses a free parameter besides the rung and leg couplings.The model is exactly solvable by means of the Bethe ansatz method.We determine the dependence on the anisotropy parameter of the phase transition between gapped and gapless spin excitations and present the phase diagram.Finally, we show that the model is a special case of a more general Hamiltonian with six free parameters.We also investigate the thermodynamics of the model.Specifically, the magnetic susceptibility as a function of the temperature is obtained numerically.The influence of this anisotropy parameter on these physical curves is determined explicitly.A comparsion between the spin gap obtained from the susceptibility curve and that one obtained from the Bethe ansatz equations is performed and a good agreement is found.
We consider a two-leg S=1/2 quantum spin ladder model with two-spin (intra-rung) and four-spin (inter-rung) Heisenberg exchange interactions and a uniform magnetic field. Exact mappings are derived connecting the partition function and correlations in the three-parameter quantum model to those known in a two-parameter Ising chain. The quantum phase diagram of the ladder magnet is determined. Static correlations provide pertinent correlation lengths and underlie spatial fluctuation behaviors at arbitrary temperatures, including quantum fluctuations at absolute zero. Dynamic correlations in zero field are used to obtain an exact solution for the inelastic neutron scattering function Sxx(q, ω) at all temperatures, explicitly yielding the elementary excitation spectrum.
We present an integrable spin-ladder model, which possesses a free parameter besides the rung coupling J. Wang's system based on the SU(4)\mathrm{SU}(4)SU(4) symmetry can be obtained as a special case. The model is exactly solvable by means of the Bethe ansatz method. We determine the dependence on the anisotropy parameter of the phase transition between gapped and gapless spin excitations and present the phase diagram. Finally, we show that the model is a special case of a more general Hamiltonian with three free parameters.
We investigate the thermodynamics of an integrable spin ladder model which possesses a free parameter besides rung and leg couplings. The model is exactly solvable by means of the Bethe ansatz and exhibits a phase transition between a gapped and a gapless spin excitation spectrum. The magnetic susceptibility is obtained numerically and its dependence on the anisotropy parameter is determined. The spin gap obtained from the susceptibility curve and the one obtained from the Bethe ansatz equations are in very good agreement. Our results for the magnetic susceptibility fit well the experimental data for the organometallic compounds (5IAP) 2 CuBr 4 ·2H 2 O (Landee C. P. et al. , Phys. Rev. B , 63 (2001) 100402(R)) Cu 2 (C 5 H 12 N 2 ) 2 Cl 4 (Hayward C. A., Poilblanc D. and Lèvy L. P., Phys. Rev. B , 54 (1996) R12649, Chaboussant G. et al. , Phys. Rev. Lett. , 19 (1997) 925; Phys. Rev. B , 55 (1997) 3046.) and (C 5 H 12 N) 2 CuBr 4 (Watson B. C. et al. , Phys. Rev. Lett. , 86 (2001) 5168) in the strong-coupling regime.