共查询到20条相似文献,搜索用时 15 毫秒
1.
Bernard Nienhuis 《Journal of statistical physics》2001,102(3-4):981-996
Tiling models are classical statistical models in which different geometric shapes, the tiles, are packed together such that they cover space completely. In this paper we discuss a class of two-dimensional tiling models in which the tiles are rectangles and isosceles triangles. Some of these models have been solved recently by means of Bethe Ansatz. We discuss the question why only these models in a larger family are solvable, and we search for the Yang–Baxter structure behind their integrability. In this quest we find the Bethe Ansatz solution of the problem of coloring the edges of the square lattice in four colors, such that edges of the same color never meet in the same vertex. 相似文献
2.
In this work, we present a proof of the existence of real and ordered solutions to the generalized Bethe Ansatz equations for the one dimensional Hubbard model on a finite lattice, with periodic boundary conditions. The existence of a continuous set of solutions extending from any U>0 to U=∞ is also shown. We use this continuity property, combined with the proof that the norm of the wavefunction obtained with the generalized Bethe Ansatz is not zero, to prove that the solution gives us the ground state of the finite system, as assumed by Lieb and Wu. Lastly, for the absolute ground state at half-filling, we show that the solution converges to a distribution in the thermodynamic limit. This limit distribution satisfies the integral equations that led to the Lieb-Wu solution of the 1D Hubbard model. 相似文献
3.
T. C. Dorlas 《Communications in Mathematical Physics》1993,154(2):347-376
A rigorous proof is given of the orthogonality and the completeness of the Bethe Ansatz eigenstates of theN-body Hamiltonian of the nonlinear Schroedinger model on a finite interval. The completeness proof is based on ideas of C.N. Yang and C.P. Yang, but their continuity argument at infinite coupling is replaced by operator monotonicity at zero coupling. The orthogonality proof uses the algebraic Bethe Ansatz method or inverse scattering method applied to a lattice approximation introduced by Izergin and Korepin. The latter model is defined in terms of monodromy matrices without writing down an explicit Hamiltonian. It is shown that the eigenfunctions of the transfer matrices for this model converge to the Bethe Ansatz eigenstates of the nonlinear Schroedinger model. 相似文献
4.
F. W. Nijhoff O. Ragnisco V. B. Kuznetsov 《Communications in Mathematical Physics》1996,176(3):681-700
An exactly integrable symplectic correspondence is derived which in a continuum limit leads to the equations of motion of the relativistic generalization of the Calogero-Moser system, that was introduced for the first time by Ruijsenaars and Schneider. For the discrete-time model the equations of motion take the form of Bethe Ansatz equations for the inhomogeneous spin-1/2 XYZ Heisenberg magnet. We present a Lax pair, the sympletic structure and prove the involutivity of the invariants. Exact solutions are investigated in the rational and hyperbolic (trigonometric) limits of the system that is given in terms of elliptic functions. These solutions are connected with discrete soliton equations. The results obtained allow us to consider the Bethe Ansatz equations as ones giving an integrable symplectic correspondence mixing the parameters of the quantum integrable system and the parameters of the corresponding Bethe wavefunction.Supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO) 相似文献
5.
The critical limit of the eight-vertex model eigenvectors obtained by means of the generalized Bethe Ansatz is shown to give the six-vertex eigenvectors as constructed in a previous paper by two of the authors. Furthermore, an explicit mapping is established between these eigenvectors and the usual Bethe Ansatz eigenvectors of the six-vertex model. This allows one to show that the indexv labeling the eight-vertex eigenstates becomes exactly the third component of the total spin in the critical limit. 相似文献
6.
The Bose-Hubbard model is a paradigm for the study of strongly correlated bosonic systems. We study the two-site Bose-Hubbard model with generic integrable open boundaries specified by the most general non-diagonal reflecting matrices. Besides the inhomogeneous parameters, the model itself has three free boundary parameters, which break the U(1)-symmetry, in other words, break the particle number conservation. The Hamiltonian H under these circumstances is constructed. With the help of the off-diagonal Bethe Ansatz method, we successfully obtain the corresponding Bethe Ansatz equations as well as the eigenvalues. 相似文献
7.
The partition function for a one-dimensional system of Bosons with repulsive delta-function interaction is investigated. We prove that if the Bethe Ansatz eigenfunctions form a complete set then the grand canonical pressure is given by the Yang-Yang formula. The proof uses a probabilistic formalism to express the partition function as an expectation with respect to a probability measure on a Banach space of measures; the asymptotic behaviour of the expectation in the thermodynamic limit is determined by the Large Deviation Principle. This method is applicable in situations in which the Hamiltonian can be diagonalised using the Bethe Ansatz. 相似文献
8.
利用量子反散射方法研究了1+1维时空中具有非对角开边界条件下的SU(2)不变Thirring模型. 于辅助空间引入独立于谱参量的规范变换,找到了适当的Fock真空态. 通过Bethe Ansatz方法得到了系统相应转移矩阵的本征值和本征态,及其谱参数所满足的Bethe Ansatz方程,并讨论了体系的边界自由度.
关键词:
SU(2)不变Thirring模型')" href="#">SU(2)不变Thirring模型
非对角开边界
量子反散射方法 相似文献
9.
J. Milewski 《Physica B: Condensed Matter》2011,406(3):520-526
The exact solution of the eigenproblem of the Heisenberg Hamiltonian for the XXX model in the case of a magnetic ring with N=5 nodes is presented in a closed algebraic form. It is demonstrated that the eigenproblem itself is expressible within the extension of the prime field Q of rationals by the primitive fifth root of unity, whereas the associated Bethe parameters, i.e. pseudomomenta, phases of scattering, and spectral parameters, require some finite field extensions, such that the nonlinearity remains algebraic rather than transcendental. Classification of exact Bethe Ansatz eigenstates in terms of rigged string configurations is presented. 相似文献
10.
The temperature-dependent susceptibility for the degenerate Anderson model with a strong correlation (U→∞) is calculated numerically on the basis of the Bethe Ansatz treatment. 相似文献
11.
I. M. Nolden 《Journal of statistical physics》1992,67(1-2):155-201
The exact solution of the asymmetric six-vertex model, published nearly without derivation by Sutherlandet al. in 1967, is rederived in detail. The transfer matrix method and the Bethe Ansatz solution for the free energy (which can be calculated from an integral equation) are discussed. For some special cases (zero or maximal polarization) the integral equation can be solved exactly. In addition, an asymptotic analysis, valid for small but nonzero polarization, is carried out. The analytical properties of the results and their relevance for the BCSOS model are discussed. 相似文献
12.
The magnetic properties of an attractive Hubbard chain are considered. Based on the Bethe Ansatz equations of the problem, exact analytic expressions are derived for the magnetization and susceptibility. These formulae can be evaluated after solving certain derivatives of the Bethe Ansatz equations. These derivative equations are also given. We give the magnetization and susceptibility curves for several values of the interaction-strength and bandfilling. We find that the susceptibility at the onset of magnetization (at the critical field) isfinite for all bandfillings, except for the cases of half filled and empty bands, and in the limit of vanishing interaction. We argue that the finiteness of the initial susceptibility is due to the fermion-like behavior of the bound pairs. We also give the gap (what is equal to the critical field) and the initial susceptibility as functions of the interaction-strength and bandfilling for the cases of nearly half filled and almost empty bands as a function of the interaction, and in the weak coupling limit as a function of the bandfilling. To our knowledge, this is the first Bethe Ansatz calculation for the gap in this latter limit. 相似文献
13.
J. F. van Diejen 《Communications in Mathematical Physics》2006,267(2):451-476
We introduce an integrable lattice discretization of the quantum system of n bosonic particles on a ring interacting pairwise via repulsive delta potentials. The corresponding (finite-dimensional) spectral problem of the integrable lattice model is solved by means of the Bethe Ansatz method. The resulting eigenfunctions turn out to be given by specializations of the Hall-Littlewood polynomials. In the continuum limit the solution of the repulsive delta Bose gas due to Lieb and Liniger is recovered, including the orthogonality of the Bethe wave functions first proved by Dorlas (extending previous work of C.N. Yang and C.P. Yang).Work supported in part by the Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT) Grant # 1051012, by the Anillo Ecuaciones Asociadas a Reticulados financed by the World Bank through the Programa Bicentenario de Ciencia y Tecnología, and by the Programa Reticulados y Ecuaciones of the Universidad de Talca. 相似文献
14.
Boris Feigin Edward Frenkel Nikolai Reshetikhin 《Communications in Mathematical Physics》1994,166(1):27-62
We propose a new method of diagonalization oif hamiltonians of the Gaudin model associated to an arbitrary simple Lie algebra, which is based on the Wakimoto modules over affine algebras at the critical level. We construct eigenvectors of these hamiltonians by restricting certain invariant functionals on tensoproducts of Wakimoto modules. This gives explicit formulas for the eigenvectors via bosonic correlation functions. Analogues of the Bethe Ansatz equations naturally appear as equations on the existence of singular vectors in Wakimoto modules. We use this construction to explain the connection between Gaudin's model and correlation functios of WZNW models. 相似文献
15.
A. Schadschneider Gang Su J. Zittartz 《Zeitschrift für Physik B Condensed Matter》1997,102(3):393-397
We extend the Bethe Ansatz solution of a onedimensional integrable fermionic model with correlated hopping to the parameter regime Δ t > 1. It is found that the model is equivalent to one with interaction 2 ? Δ t, but with twisted boundary conditions. Apart from the ground state energy we investigate the low-lying excitations and the asymptotic behaviour of the correlation functions. As in the ease of Δt < 1 we find dominating superconducting correlations for small doping. The behaviour in this regime therefore differs from that of the non-integrable model with symmetric bond-charge interaction (Hirsch model). 相似文献
16.
Kouichi Takemura 《Communications in Mathematical Physics》2003,235(3):467-494
We propose and develop the Bethe Ansatz method for the Heun equation. As an application, holomorphy of the perturbation for
the BC
1
Inozemtsev model from the trigonometric model is proved.
Received: 28 September 2001 / Accepted: 31 October 2002 Published online: 31 January 2003
Communicated by L. Takhtajan 相似文献
17.
Piotr Garbaczewski 《Annals of Physics》1982,139(2):293-313
Previously we have found that the semiclassical sine-Gordon/Thirring spectrum can be received in the absence of quantum solitons via the spin approximation of the quantized sine-Gordon system on a lattice. Later on, we have recovered the Hilbert space of quantum soliton states for the sine-Gordon system. In the present paper we present a derivation of the Bethe Ansatz eigenstates for the generalized ice model in this soliton Hilbert space. We demonstrate that via “Wick rotation” of a fundamental parameter of the ice model one arrives at the Bethe Ansatz eigenstates of the quantum sine-Gordon system. The latter is a “local transition matrix” ancestor of the conventional sine-Gordon /Thirring model, as derived by Faddeev et al. within the quantum inverse-scattering method. Our result is essentially based on the N < ∞, Δ = 1, m ? 1 regime. Consequently, the spectrum received, though resembling the semiclassical one, does not coincide with it at all. 相似文献
18.
Davide Masoero 《Letters in Mathematical Physics》2010,94(2):151-164
We introduce a new tool, the Deformed TBA (Deformed Thermodynamic Bethe Ansatz), to analyze the monodromy problem of the cubic
oscillator. The Deformed TBA is a system of five coupled nonlinear integral equations, which in a particular case reduces
to the Zamolodchikov TBA equation for the three-state Potts model. Our method generalizes the Dorey–Tateo analysis of the
(monomial) cubic oscillator. We introduce a Y-system corresponding to the Deformed TBA and give it an elegant geometric interpretation. 相似文献
19.
20.
Anindya Ghose Choudhury Asesh Roy Chowdhury 《International Journal of Theoretical Physics》2002,41(2):321-330
A new integrable long-range model is derived from a new asymmetric R-matrix recently discussed by Bibikov in relation to a XXZ spin chain in an external magnetic field. The algebraic Bethe Ansatz is used to derive the eigenvalues and equations for the eigen momenta both for the usual and long-range model. 相似文献