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Integrable models and quantum spin ladders: comparison between theory and experiment for the strong coupling ladder compounds  [PDF]
M. T. Batchelor,X. -W. Guan,N. Oelkers,Z. Tsuboi
Physics , 2005, DOI: 10.1080/00018730701265383
Abstract: (abbreviated) This article considers recent advances in the investigation of the thermal and magnetic properties of integrable spin ladder models and their applicability to the physics of real compounds. The ground state properties of the integrable two-leg spin-1/2 and the mixed spin-(1/2,1) ladder models at zero temperature are analyzed by means of the Thermodynamic Bethe Ansatz. Solving the TBA equations yields exact results for the critical fields and critical behaviour. The thermal and magnetic properties of the models are investigated in terms of the recently introduced High Temperature Expansion method, which is discussed in detail. It is shown that in the strong coupling limit the integrable spin-1/2 ladder model exhibits three quantum phases: (i) a gapped phase in the regime $HH_{c2}$, and (iii) a Luttinger liquid magnetic phase in the regime $H_{c1}
Integrable Impurity Spin Ladder Systems  [PDF]
Arlei Prestes Tonel,Angela Foerster,Xi-Wen Guan,Jon Links
Physics , 2001,
Abstract: Two integrable spin ladder systems with different types of impurities are proposed. The impurities are introduced in such a way that the integrability of the models is not violated. The models are solved exactly and the Bethe ansatz equations as well as the energy eigenvalues are obtained. We show for both models that a phase transition between gapped and gapless spin excitations occurs at a critical value of the rung coupling J. In addition, the dependence of the impurities on this phase transition is determined explicitly. Remarkably, in one of the models a decreasing of the spin gap with increasing impurity strength is found.
Integrable Stochastic Ladder Models  [PDF]
Sergio Albeverio,Shao-Ming Fei
Physics , 2001, DOI: 10.1088/0305-4470/34/34/301
Abstract: A general way to construct ladder models with certain Lie algebraic or quantum Lie algebraic symmetries is presented. These symmetric models give rise to series of integrable systems. It is shown that corresponding to these SU(2) symmetric integrable ladder models there are exactly solvable stationary discrete-time (resp. continuous-time) Markov processes with transition matrices (resp. intensity matrices) having spectra which coincide with the ones of the corresponding integrable models.
Multi-leg integrable ladder models  [PDF]
D. Arnaudon,A. Sedrakyan,T. Sedrakyan
Physics , 2002, DOI: 10.1016/j.nuclphysb.2003.11.004
Abstract: We construct integrable spin chains with inhomogeneous periodic disposition of the anisotropy parameter. The periodicity holds for both auxiliary (space) and quantum (time) directions. The integrability of the model is based on a set of coupled Yang-Baxter equations. This construction yields P-leg integrable ladder Hamiltonians. We analyse the corresponding quantum group symmetry.
The Physical Basis of Integrable Spin Models  [PDF]
Indrani Bose
Physics , 2002,
Abstract: Integrable models are often constructed with real systems in mind. The exact solvability of the models leads to results which are unambiguous and provide the correct physical picture. In this review, we discuss the physical basis of some integrable spin models and their relevance in the study of real systems. The emphasis in the review is on physical understanding rather than on the mathematical aspects of integrability.
Thermodynamic properties of an integrable quantum spin ladder with boundary impurities  [PDF]
M. T. Batchelor,X. -W. Guan,A. Foerster,A. P. Tonel,H. -Q. Zhou
Physics , 2003, DOI: 10.1016/j.nuclphysb.2003.07.012
Abstract: An integrable quantum spin ladder based on the SU(4) symmetry algebra with boundary defects is studied in the framework of boundary integrability. Five nontrivial solutions of the reflection equations lead to different boundary impurities. In each case the energy spectrum is determined using the quantum inverse scattering method. The thermodynamic properties are investigated by means of the thermodynamic Bethe ansatz. In particular, the susceptibility and the magnetization of the model in the vicinity of the critical points are derived along with differing magnetic properites for antiferromagnetic and ferromagnetic impurity couplings at the edges. The results are applicable to the strong coupling ladder compounds, such as Cu_2(C_5 H_12 N_2)_2 Cl_4.
Magnetic Susceptibility of an integrable anisotropic spin ladder system  [PDF]
A. P. Tonel,S. R. Dahmen,A. Foerster,A. L. Malvezzi
Physics , 2003, DOI: 10.1209/epl/i2003-00144-3
Abstract: We investigate the thermodynamics of a spin ladder model which possesses a free parameter besides the rung and leg couplings. The model is exactly solved by 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. A connection with the compounds KCuCl3, Cu2(C5H12N2)2Cl4 and (C5H12N)2CuBr4 in the strong coupling regime is made and our results for the magnetic susceptibility fit the experimental data remarkably well.
Ground state energy and mass gap of a generalised quantum spin ladder  [PDF]
M. T. Batchelor,M. Maslen
Physics , 1999, DOI: 10.1088/0305-4470/33/3/301
Abstract: We show that a 2-leg ladder hamiltonian introduced recently by Albeverio and Fei (cond-mat/9807341) can be made to satisfy the Hecke algebra. As a result we have found an equivalent representation of the eigenspectrum in terms of the spin-1/2 antiferromagnetic XXZ chain at $\Delta = - 5/3$. The values of thermodynamic quantities such as the ground state energy and mass gap follow from the known XXZ results.
Ladder Operators for Integrable One-Dimensional Lattice Models  [PDF]
M. Takizawa,J. Links
Physics , 2002,
Abstract: A generalised ladder operator is used to construct the conserved operators for any model derived from the Yang-Baxter equation. As an example, the low order conserved operators for the XYh model are calculated explicitly.
Integrable discretizations of the spin Ruijsenaars-Schneider models  [PDF]
O. Ragnisco,Yu. B. Suris
Physics , 1996, DOI: 10.1063/1.532114
Abstract: Integrable discretizations are introduced for the rational and hyperbolic spin Ruijsenaars--Schneider models. These discrete dynamical systems are demonstrated to belong to the same integrable hierarchies as their continuous--time counterparts. Explicit solutions are obtained for arbitrary flows of the hierarchies, including the discrete time ones.
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