Book contents
- Frontmatter
- Contents
- Foreword
- Translator's note
- Introduction
- 1 The chain of spin-1/2 atoms
- 2 Thermodynamic limit of the Heisenberg–Ising chain
- 3 Thermodynamics of the spin-1/2 chain: Limiting cases
- 4 δ-Interacting bosons
- 5 Bethe wavefunctions associated with a reflection group
- 6 Continuum limit of the spin chain
- 7 The six-vertex model
- 8 The eight-vertex model
- 9 The eight-vertex model: Eigenvectors and thermodynamics
- 10 Identical particles with δ-interactions
- 11 Identical particles with δ-interactions: General solution for two internal states
- 12 Identical particles with δ-interactions: General solution for n components and limiting cases
- 13 Various corollaries and extensions
- 14 On the Toda chain
- References
- Index
- References
References
Published online by Cambridge University Press: 05 April 2014
Translated by
Book contents
- Frontmatter
- Contents
- Foreword
- Translator's note
- Introduction
- 1 The chain of spin-1/2 atoms
- 2 Thermodynamic limit of the Heisenberg–Ising chain
- 3 Thermodynamics of the spin-1/2 chain: Limiting cases
- 4 δ-Interacting bosons
- 5 Bethe wavefunctions associated with a reflection group
- 6 Continuum limit of the spin chain
- 7 The six-vertex model
- 8 The eight-vertex model
- 9 The eight-vertex model: Eigenvectors and thermodynamics
- 10 Identical particles with δ-interactions
- 11 Identical particles with δ-interactions: General solution for two internal states
- 12 Identical particles with δ-interactions: General solution for n components and limiting cases
- 13 Various corollaries and extensions
- 14 On the Toda chain
- References
- Index
- References
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- The Bethe Wavefunction , pp. 314 - 322Publisher: Cambridge University PressPrint publication year: 2014
References
1977. Some finite dimensional integrable systems and their scattering behavior. Commun. Math. Phys., 55, 195–230.Google Scholar
1969. Commun. Math. Phys., 14, 120–157.
and 1977a. Explicit Plancherel theorem for ground state representation of the Heisenberg chain. Proc. Nat. Acad. Sci. USA, 74(3), 816–817.Google Scholar
and 1977b. Ground state representation of the infinite one-dimensional Heisenberg ferromagnet. II. An explicit Plancherel formula. Commun. Math. Phys., 54, 255–278.Google Scholar
and 1978. Ground state representation of the ininite one-dimensional Heisenberg ferromagnet. III. Scattering theory. J. Math. Phys., 19(8), 1699–1704.Google Scholar
, and 1983. Analysis of the Bethe ansatz equations of the XXZ model. Nucl. Phys. B, 220, 13–34.Google Scholar
and 1973. On the spontaneous order of the eight-vertex model. J. Phys. C: Solid St. Phys., 6(20), 2913.Google Scholar
1972. In: and (eds), Phase Transitions and Critical Phenomena, Vol. IV. London: Academic Press.
1977. Nonlinear Equations in Physics and Mathematics. Dordrecht: Reidel.
1970b. Three-colorings of the square lattice: A hard squares model. J. Math. Phys., 11(10), 3116–3124.Google Scholar
1971b. Generalized ferroelectric model on the square lattice. Stud. App. Math., 50, 51.Google Scholar
1972b. Partition function of the eight-vertex lattice model. Ann. Phys., 70(1), 193–228.Google Scholar
1973a. Asymptotically degenerate maximum eigenvalues of the eight-vertex model transfer matrix and interfacial tension. J. Stat. Phys., 8, 25–55.Google Scholar
1973b. Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain. I. Some fundamental eigenvectors. Ann. Phys, 76(1), 1–24.Google Scholar
1973c. Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain. II. Equivalence to a generalized ice-type lattice model. Ann. Phys., 76(1), 25–47.Google Scholar
1973d. Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain. III. Eigenvectors of the transfer matrix and Hamiltonian. Ann. Phys., 76(1), 48–71.Google Scholar
1973e. Spontaneous staggered polarization of the F model. J. Phys. C: Sol. St. Phys., 6(5), L94.Google Scholar
1978. Solvable eight-vertex model on an arbitrary planar lattice. Phil. Trans. Roy. Soc. London A, 289(1359), 315–346.Google Scholar
1979. Exact solution of the two-dimensional model with asymptotic freedom. Phys. Lett. B, 87, 117–121.Google Scholar
and 1979a. Method for solving the massive Thirring model. Phys. Rev. Lett., 42, 135–138.Google Scholar
and 1979b. Structure and solution of the massive Thirring model. Phys. Rev. D, 19, 3666–3681.Google Scholar
1931. Zur Theorie der Metalle. I. Eigenwerte und Eigenfunktionen der linearen Atomkette. Zeit. für Physik, 71, 205.Google Scholar
and 1980. Nonlinear Schrödinger equation, Backhand transformations and Painlevé transcendents. Il Nuovo Cimento B, 59, 40–58.Google Scholar
1968. Numerical studies on the linear Ising-Heisenberg model. Ph.D. thesis, University of London.
and 1964. Linear magnetic chains with anisotropic coupling. Phys. Rev., 135(3A), A640–A658.Google Scholar
and 1966. Un problème à N corps soluble. C. R. Acad. Sci. Paris, sér. A-B, 263, 670–673.Google Scholar
, , and 1979. Remarks about the existence of non-local charges in two-dimensional models. Phys. Lett. B, 82(3&4), 442–444.Google Scholar
, and 1966. Possibility of superconductivity type phenomena in a one-dimensional system. Sov. Phys. JETP, 23, 489–501.Google Scholar
1971. Solution of the one-dimensional N-body problems with quadratic and/or inversely quadratic pair potentials. J. Math. Phys., 12(3), 419–436.Google Scholar
1978. Integrable many-body problems. In: (ed.), Nonlinear Equations in Physics and Mathematics. Dordrecht: Reidel. Proceedings of the NATO Advanced Study Institute held in Istanbul, August 1977.
1981. Matrices, differential operators, and polynomials. J. Math. Phys., 22(5), 919–934.Google Scholar
, and 1975. Exact solution of the classical and quantal one-dimensional many-body problems with the two-body potential V (x) = g2a2 sinh-2 ax. Lett. al Nuovo Cimento, 13, 383–387.Google Scholar
and 1980. Zakharov-Shabat-Mikhailov scheme of construction of two-dimensional completely integrable field theories. Zeit. für Physik C, 5, 55–62.Google Scholar
and 1982. Hamiltonian structure of isospectral deformation equations. Elliptic curve case. In: and (eds), The Riemann Problem, Complete Integrability and Arithmetic Applications. Lecture Notes in Mathematics, Vol. 925. Berlin: Springer-Verlag; pp. 134–146.
1975. Quantum sine-Gordon equation as the massive Thirring model. Phys. Rev. D, 11, 2088–2097.Google Scholar
1948. Regular Polytopes. London: Methuen.
and 1972. Generators and Relations for Discrete Groups, 3rd edn. Berlin: Springer-Verlag.
, and 1975. Particle spectrum in model field theories from semiclassical functional integral techniques. Phys.Rev.D, 11, 3424–3450.Google Scholar
1976. Solution d'un modèle à trois corps: étude de la dissusion. Ph.D. thesis, Université Paris.
1966. A soluble Fermi-gas model. Validity of transformations of the Bogoliubov type. J. Math. Phys., 7(12), 2136–2144.Google Scholar
and 1962. Spin-wave spectrum of the antiferromagnetic linear chain. Phys. Rev., 128(5), 2131–2135.Google Scholar
1967. The Principles of Quantum Mechanics, 4th edn (revised). Oxford: Oxford University Press.
1962. Statistical theory of the energy levels of complex systems. I. J. Math. Phys., 3(1), 140–156.Google Scholar
1976. Fredholm determinants and inverse scattering problems. Commun. Math. Phys., 47, 171–183.Google Scholar
and 1974. Correlation functions for a one-dimensional Fermi system with long-range interaction (Tomonaga model). Sov. Phys. JETP, 38. Russian original: ZhETF, Vol. 65, No. 1, p. 411, January 1974.Google Scholar
1980. Quantum completely integrable models of ield theory. In: Mathematical Physics Review Section C, Vol. 107. New York: Harwood Academic; p. 155.
1980. The factorizable S matrix for the particles with different parity and integrable anisotropic spin chain with spin one. Technical Report CERN, Ref. TH 2963.
1968. In: Proceedings of the International Conference on Statistical Mechanics, Kyoto.
1969. J. Phys. Soc. Japan Suppl., 26, 87.
1980. Solitons and magnons in the classical Heisenberg chain. J. Phys. A: Math. Gen., 13(4), 1467.Google Scholar
1880. Über das Additions-theorem der Thetafunktionen mehrerer Variabeln. J. reine angew. Math., 89, 185.Google Scholar
1968. Gesammelte Abhandlungen, Band II. Berlin: Springer-Verlag.
1967a. Étude d'une modèle à une dimension pour un système de fermions en interaction. Ph.D. thesis, Université Paris. CEA Report No. 5-3569 (1968).
1967b. Un systeme à une dimension de fermions en interaction. Phys. Lett. A, 24(1), 55–56.Google Scholar
1971a. Bose gas in one dimension. I. The closure property of the scattering wavefunctions. J. Math. Phys., 12(8), 1674–1676.Google Scholar
1971b. Bose gas in one dimension. II. Orthogonality of the scattering states. J. Math. Phys., 12(8), 1677–1680.Google Scholar
1971d. Thermodynamics of the Heisenberg-Ising ring for Δ ≥ 1. Phys. Rev. Lett., 26(21), 1301–1304.Google Scholar
(1) 1972; (2) 1973. Modèles exacts en mécanique statistique: la méthode de Bethe et généralisations. Technical Report, CEA Saclay.
1976. Diagonalisation d'une classe d'Hamiltoniens de spin. J. Physique, 37, 1087–1098.Google Scholar
1978. Sur le problème de deux ou trois électrons en présence d'un moment localisé. J. Physique, 39, 1143–1168.Google Scholar
, and 1981. Normalization sum for the Bethe's hypothesis wave functions of the Heisenberg-Ising chain. Phys. Rev. D, 23, 417–419.Google Scholar
1960. Relationship between systems of impenetrable bosons and fermions in one dimension. J. Math. Phys., 1(6), 516–523.Google Scholar
and 1964. Order-Disorder Phenomena. New York: Wiley-Interscience.
1964. Magnetization curve at zero temperature for the antiferromagnetic Heisenberg linear chain. Phys. Rev., 133(3A), A768–A775.Google Scholar
and 1979. Completely integrable systems and groups generated by reflections. Proc. Nat. Acad. Sci. USA, 76, 6057–6059.Google Scholar
1964. Group Theory and its Application to Physical Problems. New York: Addison-Wesley.
1881. Handbuch der Kugelfunktionen II, 2nd edn. Berlin: Springer-Verlag; p. 472.
1981. Rigorous derivation of the distribution of the eigenstates of the quantum Heisenberg-Ising chain with XY-like anisotropy. Phys. Lett. A, 84(6), 338–340.Google Scholar
1973. Exact N-soliton solution of a nonlinear lumped network equation. J. Phys. Soc. Japan, 35(1), 286–288.Google Scholar
and 1976. A variety of nonlinear network equations generated from the Bäcklund transformation for the Toda lattice. Prog. Theor. Phys. Suppl., 59, 64–100.Google Scholar
and 1979. Calculation of the S-matrix from the Hamiltonian of the massive Thirring model. Technical Report, Université Fribourg.
1963. The circular plate condenser at small separations. Proc. Camb. Phil. Soc., 59, 211.Google Scholar
1978. Factorization of the multiparticle S matrix in two-dimensional space-time models. Phys. Rev. D, 18, 1275–1285.Google Scholar
and 1981. The inverse scattering method approach to the quantum Shabat-Mikhailov model. Commun. Math. Phys., 79, 303–316.Google Scholar
, , and 1980. Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent. Phys. D, 1(1), 80–158.Google Scholar
and 1972. Low-temperature thermodynamics of the | Δ | ≥ 1 Heisenberg-Ising ring. Phys.Rev. A, 6, 1613–1626.Google Scholar
, and 1973. Vertical-arrow correlation length in the eight-vertex model and the low-lying excitations of the X-Y-Z Hamiltonian. Phys. Rev. A, 8(5), 2526–2547.Google Scholar
1955. Mathematical analysis of a simple model for the stripping reaction. Zeit. für Angew. Math. Phys., 6, 316–326.Google Scholar
and 1971. Some critical properties of the eight-vertex model. Phys.Rev.B, 4, 3989–3993.Google Scholar
, , , and 1977. On the uniqueness of a purely elastic S-matrix in (1+1) dimensions. Phys. Lett. B, 67(3), 321–322.Google Scholar
1967. Graph theory and crystal physics. In: (ed.), Graph Theory and Theoretical Physics. New York: Academic Press.
1980. The mass spectrum and the S-matrix of the massive Thirring model in the repulsive case. Commun. Math. Phys., 76, 165–176.Google Scholar
1979. Generalized Bethe ansatz and quantum inverse problem method. Preprint, Leningrad Branch of the Mathematics Institute, Leningrad.
and 1979. Quantum inverse scattering method and the Heisenberg ferromagnet. Phys. Lett. A, 70(5&6), 461–463.Google Scholar
, and 1981. Yang-Baxter equation and representation theory: I. Lett. Math. Phys., 5, 393–403.Google Scholar
1974. Lattice gas with nearest-neighbor interaction in one dimension with arbitrary statistics. J. Math. Phys., 15(10), 1675–1676.Google Scholar
1977. Continuum spin system as an exactly solvable dynamical system. Phys. Lett. A, 61(1), 53–54.Google Scholar
1968. Integrals of nonlinear equations of evolution and solitary waves. Commun. Pure Appl. Math., 21(5), 467–490.Google Scholar
1964. Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. J. Math. Phys., 5(7), 930–943.Google Scholar
and 1970. On the capacity of the circular disc condenser at small separation. Proc. Camb. Phil. Soc., 68, 235.Google Scholar
1963. Exact analysis of an interacting Bose gas. II. The excitation spectrum. Phys. Rev., 130(4), 1616–1624.Google Scholar
1967a. Exact solution of the F model of an antiferroelectric. Phys. Rev. Lett., 18, 1046–1048.Google Scholar
1967b. Exact solution of the problem of the entropy of two-dimensional ice. Phys. Rev. Lett., 18, 692–694.Google Scholar
1967c. Exact solution of the two-dimensional Slater KDP model of a ferroelectric. Phys. Rev. Lett., 19, 108–110.Google Scholar
and 1963. Exact analysis of an interacting Bose gas. I. The general solution and the ground state. Phys. Rev., 130(4), 1605–1616.Google Scholar
and 1962. Theory of ferromagnetism and the ordering of electronic energy levels. Phys. Rev., 125(1), 164–172.Google Scholar
and (eds). 1966. Mathematical Physics in One Dimension. New York: Academic Press.
and 1968. Absence of Mott transition in an exact solution of the short-range, one-band model in one dimension. Phys. Rev. Lett., 20(25), 1445–1448.Google Scholar
and 1972. Two dimensional ferroelectric models. In: and (eds), Critical Phenomena and Phase Transitions. New York: Academic Press.
, and 1961. Two soluble models of an antiferromagnetic chain. Ann. Phys., 16, 407–466.Google Scholar
1973. One-dimensional model of the rearrangement and dissociation processes. Probability amplitudes and cross-sections. Acta Phys. Polon., 44, 115–137.Google Scholar
1974. One-dimensional model of the rearrangement process and the Faddeev equations. J. Math. Phys., 15(1), 133–138.Google Scholar
1980. On the application of the Sommerfeld-Maluzhinetz transformation to some one-dimensional three-particle problems. J. Math. Phys., 21(5), 1092–1102.Google Scholar
and 1975. Calculation of critical exponents in two dimensions from quantum field theory in one dimension. Phys. Rev. B, 12(9), 3908–3917.Google Scholar
1963. An exactly soluble model of a many-fermion system. J. Math. Phys., 4(9), 1154–1162.Google Scholar
and 1965. Exact solution of a many-fermion system and its associated boson field. J. Math. Phys., 6, 304–312.Google Scholar
and 1968. Hydrogen-bonded crystals and the anisotropic Heisenberg chain. Nuovo Cimento B, 56, 311–315.Google Scholar
and 1973. The Two-dimensional Ising Model. Cambrdige, MA: Harvard University Press.
1964. Study of exactly soluble one-dimensional N-body problems. J. Math. Phys., 5(5), 622–636.Google Scholar
1965. Interacting fermions in one dimension. I. Repulsive potential. J. Math. Phys., 6(3), 432–439.Google Scholar
1966. Interacting fermions in one dimension. II. Attractive potential. J. Math. Phys., 7(1), 123–132.Google Scholar
and 1972. The scattering of three impenetrable particles in one dimension. J. Math. Phys., 13(10), 1595–1607.Google Scholar
1980. Random Matrices. New York: Academic Press.
1964. Integral Equations. Oxford: Pergamon Press.
1966. A Treatise on the Theory of Determinants (1933). New York: Dover.
1966. Lattice statistics of hydrogen bonded crystals. I. The residual entropy of ice. J. Math. Phys., 7(8), 1484–1491.Google Scholar
1961. Soluble model of a break-up process. Proc. Roy. Soc. London A, 264(1318), 408–430.Google Scholar
1944. Crystal statistics. I. A two-dimensional model with an order-disorder transition. Phys. Rev., 65, 117–149.Google Scholar
and 1960. Corso: Thermodinamica dei processi irreversibili. In: Rendiconti della Scuola internazionale di Fisica (Enrico Fermi) X. Societa Italiana di Fisica, Bologna.
1958. Linear antiferromagnetic chain with anisotropic coupling. Phys. Rev., 112(2), 309–316.Google Scholar
1967. Complexes of several spins in a linear Heisenberg chain. Sov. Phys. JETP Lett., 5, 48.Google Scholar
1969. Excitation spectrum of an antiferromagnetic Heisenberg chain. Sov. Phys. JETP, 29, 727.Google Scholar
1970. Excitation spectrum in the one-dimensional Hubbard model. Sov. Phys. JETP, 30, 1160.Google Scholar
1960. The Nature of the Chemical Bond, 3rd edn. Ithaca, NY: Cornell University Press.
1971. Combinatorial Methods. New York: Springer-Verlag.
1976. Integrable Hamiltonian systems and interactions through quadratic constraints. Commun. Math. Phys., 46, 207–221.Google Scholar
1965. Exact eigenstates of the pairing-force Hamiltonian. II. J. Math. Phys., 6(7), 1034–1051.Google Scholar
1980a. On one-dimensional integrable quantum systems with ininitely many degrees of freedom. Ann. Phys., 128(2), 335–362.Google Scholar
1980b. The continuum limit of the infinite isotropic Heisenberg chain in its ground state representation. J. Funct. Anal., 39(1), 75–84.Google Scholar
, and 1976. Towards an explicit construction of the sine-Gordon ield theory. Phys. Lett. B, 63(4), 422–424.Google Scholar
1950. Théorie des distributions. Paris: Hermann.
1969. Topics in Complex Function Theory. New York: Wiley-Interscience.
1973. Topics in Complex Function Theory, 2nd edn. New York: Wiley-Interscience.
1966. Mixed Boundary Value Problems in Potential Theory. Amsterdam: North-Holland.
1968. Further results for the many-body problem in one dimension. Phys. Rev. Lett., 20(3), 98.Google Scholar
1970. Two-dimensional hydrogen bonded crystals without the ice rule. J. Math. Phys., 11(11), 3183–3186.Google Scholar
1971. Quantum many-body problem in one dimension: thermodynamics. J. Math. Phys., 12(2), 251–256.Google Scholar
1980. Nondiffractive scattering: Scattering from kaleidoscopes. J. Math. Phys., 21(7), 1770–1775.Google Scholar
, and 1967. Exact solution of a model of two-dimensional ferroelectrics in an arbitrary external electric field. Phys. Rev. Lett., 19, 588.Google Scholar
1939. Orthogonal Polynomials. Rhode Island: American Mathematical Society.
1971. One-dimensional Heisenberg model at inite temperature. Prog. Theor. Phys., 46(2), 401–415.Google Scholar
and 1972. One-dimensional anisotropic Heisenberg model at finite temperatures. Prog. Theor. Phys., 48(6), 2187–2209.Google Scholar
and 1974. Essentially nonlinear one-dimensional model of classical field theory. Theor. Math. Phys., 21, 1046–1057.Google Scholar
1977. Integration of the continuous Heisenberg spin chain through the inverse scattering method. Phys. Lett. A, 64(2), 235–237.Google Scholar
1980. Quantum inverse method for two-dimensional ice and ferroelectric lattice models. J. Math. Phys., 21(5), 1115–1117.Google Scholar
1981. Exact integrability in quantum ield theory and statistical systems. Rev. Mod. Phys., 53(2), 253–285.Google Scholar
1977. Ground state representation of the ininite one-dimensional Heisenberg ferromagnet, I. J. Math. Anal. Appl., 59(2), 392–414.Google Scholar
1939. The Theory of Functions, 2nd edn. London: Oxford University Press.
and 1979. One-particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Phys. Rev. Lett., 42, 3–6.Google Scholar
1935. Elementary Theory of Invariants. Princeton, NJ: Princeton University Press.
and 1927. A Course of Modern Analysis, 4th edn. Cambridge: Cambridge University Press.
1981. Exact solution of the s-d exchange model (Kondo problem). J. Phys. C: Solid State Phys., 14(10), 1463.Google Scholar
1982. On the S = 0 excited states of an anisotropic Heisenberg chain. J. Phys. A., 15, 2985–2996.Google Scholar
1952. The spontaneous magnetization of a two-dimensional Ising model. Phys. Rev., 85, 808–816.Google Scholar
1967. Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Phys. Rev. Lett., 19(23), 1312–1315.Google Scholar
1968. S matrix for the one-dimensional N-body problem with repulsive or attractive δ-function interaction. Phys. Rev., 168, 1920–1923.Google Scholar
and 1966a. Ground-state energy of a Heisenberg-Ising lattice. Phys. Rev., 147, 303–306.Google Scholar
and 1966b. One-dimensional chain of anisotropic spin-spin interactions. I. Proof of Bethe's hypothesis for ground state in a inite system. Phys. Rev., 150(1), 321–327.Google Scholar
and 1966c. One-dimensional chain of anisotropic spin-spin interactions. II. Properties of the ground-state energy per lattice site for an ininite system. Phys. Rev., 150(1), 327–339.Google Scholar
and 1966d. One-dimensional chain of anisotropic spin-spin interactions. III. Applications. Phys. Rev., 151(1), 258–264.Google Scholar
and 1969. Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. J. Math. Phys., 10(7), 1115–1122.Google Scholar
1967. Exact solution of a model of two-dimensional ferroelectrics in an arbitrary external electric field. Phys. Rev. Lett., 19, 586–588.Google Scholar
and 1972. Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in non-linear media. Sov. Phys. JETP, 34(1), 62.Google Scholar
1977. Exact two-particle S-matrix of quantum sine-Gordon solitons. Commun. Math. Phys., 55, 183–186.Google Scholar
1979. Z4-symmetric factorized S-matrix in two space-time dimensions. Commun. Math. Phys., 69, 165–178.Google Scholar
1980. Tetrahedra equations and integrable systems in three-dimensional space. Sov. Phys. JETP, 52(2), 325.Google Scholar
and 1978. Relativistic factorized S-matrix in two dimensions having O (N) isotopic symmetry. Nucl. Phys. B, 133(3), 525–535.Google Scholar