Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Birkhäuser-Verlag eBooks

MathPhys odyssey 2001 : integrable models and beyond : in honor of Barry M. McCoy

Masaki Kashiwara, 哲二 三輪, Barry M. McCoy

Published Jan 1, 2002• 2 citations
OpenAlex

Abstract

Preface * Wavevector-Dependent Susceptibilities in Aperiodic Planar Models * Correlation Functions and Susceptibility in the Z-Invariant Ising Model * A Rapidity-independent Parameter in the Star-Triangle Relation * Evaluation of Integrals Representing Correlations in XXX Heisenberg Spin Chain * A Note on Quotients of the Onsager Algebra * Evaluation Parameters and Bethe Roots for the Six Vertex Model at Roots of Unity * Normalization Factors, Reflection Amplitudes and Integrable Systems * Vertex Operator Algebra Arising from the Minimal Series M(3,p) and Monomial Basis * Paths Crystals and Fermionic Formulae * The Nonlinear Steepest Descent Approach to the Asymtpotis of the Second Painleve Transcendent in the Complex Domain * Generalized Umemura Polynomials and Hirota-Miwa Equation * Correlation Functions of Quantum Integrable Models: The XXZ Spin Chain * On Form Factors of SU(2) Invariant Thirring Model * Integrable Boundaries and Universal TBA Functional Equations * Conformal Field Theories, Graphs and Quantum Algebras * q-Supernomial Coefficients: From Rigging to Ribbons * Separation of Variables for Quantum Integrable Models Related to Uq(slN) * On a Distribution Function Arising in Computational Biology

Related papers

Statistical models, Yang-Baxter equation and related topics : proceedings of the satellite meetings of STATPHYS-19, Tianjin, China, 8-10 August 1995 ; and Symmetry, statistical mechanical models and applciations : proceedings of the Seventh Nankai Workshop, Tianjin, China, 12-13 August 1995

Mo‐Lin Ge, Fa Yueh Wu

Part 1 Satellite meeting of Statphys-19: quantum domains in ferromagnetic anisotropic Heisenberg chains, F.C. Alcaraz et al algebraic solution of the coincidence problem for crystals and quasi crystals, M. Baake reflection equations and surface critical phenomena, M.T. Batchelor quantum field theories in terms of group-valued local fields - an overview, L.L. Chau U(1)-invariant local and integrable lattice formulation of the massive Thirring model, C. Destri dilute algebras and solvable lattice models, U. Grimm quantum group and the Hofstadter problem, Y. Hatsugai et al domain walls in the spin-S quantum Ising chain, M. Henkel mutual exclusion statistics in the exactly solvable model of the Mott metal-insulator transition, M. Kohmoto et al boundary Yang-Baxter in the RSOS/SOS representation, W.M. Koo and C. Ahn probability of phase separation and two point temperature correlation functions for the Bose gas with delta interaction, V.E. Korepin and A.R. Its the generalized chiral clock model and its phase diagram, H. Au-Yang and J.H.H. Perk stochastic reaction-diffusion processes, operator algebras and integrable quantum spin chains, G.M. Schutz vertex-face correspondence in elliptic solutions of the Yang-Baxter equation, Y. Shibukawa logarithmic anomalies of susceptibility for solvable models, M. Takahashi on chiral Hubbard model at strong interaction, D.F. Wang soluble free-fermion models in d dimensions, F.Y. Wu bosonization based on Bethe Ansatz equations and proof of the conformal conjecture, Y.S. Wu and Y Yu. Part 3 The seventh Nankai workshop: one dimensional lattice models of electrons with r2 hopping and exchange, Ch. Gruber and D.F. Wang symmetry group invariants for spontaneous magnetization, J.-M. Maillard Zamolodchikov-Faddeev algebra vertex models, H.-P. Eckle scaling properties of the Ising model in a field, U. Grimm and B. Nienhuis experimental realizations of integrable reaction-diffusion processes in biological and chemical systems, G.M. Schutz and other papers. (Part contents).

WORLD SCIENTIFIC eBooks•Jan 1, 1996•0 citations

Quantum integrable systems

Steve Zelditch

NONLINEAR SYSTEMS AND CLASSICAL IST Introduction Definition of Integrability Lax Pair Technique Inverse Scattering Transform Hamiltonian Structure COORDINATE BETHE ANSATZ Introduction Nonlinear Systems and the CBA Fermionic System Boundary Condition in Bethe Ansatz Heisenberg Spin Chain Spin of the Bethe Ansatz State Other Integrable Models YANG-BAXTER EQUATION Introduction General Description Factorized Scattering Baxter's Star Triangle Relation Vertex Models Reflection Equation Algebra CONTINUOUS INTEGRABLE SYSTEMS Introduction Quantum Continuous Integrable Systems Conserved Quantities Nonultralocal systems and the YBE Operator Product Expansion and YBE Finite Boundary Conditions Modified Classical Yang-Baxter Equation ALGEBRAIC BETHE ANSATZ Introduction Discrete Self Trapping Model Asymmetric XXZ Model in a Magnetic Field Analytical Bethe Ansatz Off-Shell Bethe Ansatz Nested Bethe Ansatz Fusion Procedure Fusion Procedure for Open chains Fusion Procedure for Transfer Matrices Application of Fusion Procedure INTEGRABLE LONG-RANGE MODELS Introduction Long-Range Models from the ABA Symmetry Transformation Calogero-Moser Models SEPARATION OF VARIABLES Introduction Hamilton-Jacobi Equation Sklyanin's Method for SoV Goryachev-Chaplygin Top Quantum Case and the Role of Lie Algebra Bi-Hamiltonian Structure and SoV SoV for GCM Model SoV and Boundary Conditions BACKLUND TRANSFORMATIONS Introduction Permutability Theorem Backlund Transformations and Classical Inverse Scattering Backlund Transformations from Riccati Equation Darboux Backlund Transformations The Exponential Lattice Canonical Transformations Group Property of Backlund Transformations Recent Developments in Backlund Transformation Theory Sklyanin's Formalism for Canonical Backlund Transformations Extended Phase Space Method Quantization of Backlund Transformations Method of Projection Operators QUANTUM GLM EQUATION Introduction Quantum GLM Equation Quantum Floquet Function Exact Quantization Quantum GLM Equation in a Continuous System Bound States and an Alternative Approach APPENDICES Direct Product Calculus Grassman Algebra Bethe Ansatz Equation AKNS Problem BIBLIOGRAPHY INDEX

Regional conference series in mathematics•Dec 12, 2017•18 citations

Drinfeld twists, symmetric Bethe vectors and correlation functions of SUSY integrable models(Fundamental Problems and Applications of Quantum Field Theory)

Yao-Zhong Zhang

素粒子論研究•Apr 20, 2006•0 citations

Evaluation Parameters and Bethe Roots for the Six-Vertex Model at Roots of Unity

K. Fabricius, Barry M. McCoy

We propose an expression for the current form of the lowering operator of the sl 2 loop algebra symmetry of the six-vertex model (XXZ spin chain) at roots of unity. This operator has poles which correspond to the evaluation parameters of representation theory which are given as the roots of the Drinfeld polynomial. We explicitly compute these polynomials in terms of the Bethe roots which characterize the highest weight states for all values of S z . From these polynomials we find that the Bethe roots satisfy sum rules for each value of S z .

arXiv:cond-mat/0108057•Birkhäuser Boston eBooks•Jan 1, 2002•43 citations

Universality and Renormalization: From Stochastic Evolution to Renormalization of Quantum Fields

Ilia A. Binder, Dirk Kreimer

Manifestly gauge invariant exact renormalization groups by S. Arnone, T. R. Morris, and O. J. Rosten SLE(8/3) and Brownian excursions in annuli by R. O. Bauer Cardy's formula on the triangular lattice, the easy way by V Beffara Rota-Baxter algebras in renormalization of perturbative quantum field theory by K. Ebrahimi-Fard and L. Guo Practicalities of renormalizing quantum field theories by J. A. Gracey Quantum field theory in curved spacetime by S. Hollands Entropy of $XY$ spin chain and block Toeplitz determinants by A. R. Its, B.-Q. Jin, and V. E. Korepin On the quantitative boundary behavior of SLE by N.-G. Kang The configurational measure on mutually avoiding SLE paths by M. J. Kozdron and G. F. Lawler Dyson-Schwinger equations: From Hopf algebra to number theory by D. Kreimer Two-sided $SLE_{8/3}$ and the infinite self-avoiding polygon by G. F. Lawler and J. R. Lind Using the renormalization gorup by D. G. C. McKeon Short distance behavior of scaling functions for the planar ising model by J. Palmer Constructing conformal field theory models by I. Todorov The art of computing loop integrals by S. Weinzierl The transition temperature of the weakly interacting Bose gas by J. Zinn-Justin.

•Feb 28, 2007•19 citations

Yang-Baxter Algebras and Integrable Models in Field Theory and Statistical Mechanics

Hector J. de Vega

Springer series in synergetics•Jan 1, 1985•1 citation
Preface * Wavevector-Dependent Susceptibilities in Aperiodic Planar Models * Correlation Functions and Susceptibility in the Z-Invariant Ising Model * A Rapidity-independent Parameter in the Star-Triangle Relation * Evaluation of Integrals Representing Correlations in XXX Heisenberg Spin Chain * A Note on Quotients of the Onsager Algebra * Evaluation Parameters and Bethe Roots for the Six Vertex Model at Roots of Unity * Normalization Factors, Reflection Amplitudes and Integrable Systems * Vertex Operator Algebra Arising from the Minimal Series M(3,p) and Monomial Basis * Paths Crystals and Fermionic Formulae * The Nonlinear Steepest Descent Approach to the Asymtpotis of the Second Painleve Transcendent in the Complex Domain * Generalized Umemura Polynomials and Hirota-Miwa Equation * Correlation Functions of Quantum Integrable Models: The XXZ Spin Chain * On Form Factors of SU(2) Invariant Thirring Model * Integrable Boundaries and Universal TBA Functional Equations * Conformal Field Theories, Graphs and Quantum Algebras * q-Supernomial Coefficients: From Rigging to Ribbons * Separation of Variables for Quantum Integrable Models Related to Uq(slN) * On a Distribution Function Arising in Computational Biology
Part 1 Satellite meeting of Statphys-19: quantum domains in ferromagnetic anisotropic Heisenberg chains, F.C. Alcaraz et al algebraic solution of the coincidence problem for crystals and quasi crystals, M. Baake reflection equations and surface critical phenomena, M.T. Batchelor quantum field theories in terms of group-valued local fields - an overview, L.L. Chau U(1)-invariant local and integrable lattice formulation of the massive Thirring model, C. Destri dilute algebras and solvable lattice models, U. Grimm quantum group and the Hofstadter problem, Y. Hatsugai et al domain walls in the spin-S quantum Ising chain, M. Henkel mutual exclusion statistics in the exactly solvable model of the Mott metal-insulator transition, M. Kohmoto et al boundary Yang-Baxter in the RSOS/SOS representation, W.M. Koo and C. Ahn probability of phase separation and two point temperature correlation functions for the Bose gas with delta interaction, V.E. Korepin and A.R. Its the generalized chiral clock model and its phase diagram, H. Au-Yang and J.H.H. Perk stochastic reaction-diffusion processes, operator algebras and integrable quantum spin chains, G.M. Schutz vertex-face correspondence in elliptic solutions of the Yang-Baxter equation, Y. Shibukawa logarithmic anomalies of susceptibility for solvable models, M. Takahashi on chiral Hubbard model at strong interaction, D.F. Wang soluble free-fermion models in d dimensions, F.Y. Wu bosonization based on Bethe Ansatz equations and proof of the conformal conjecture, Y.S. Wu and Y Yu. Part 3 The seventh Nankai workshop: one dimensional lattice models of electrons with r2 hopping and exchange, Ch. Gruber and D.F. Wang symmetry group invariants for spontaneous magnetization, J.-M. Maillard Zamolodchikov-Faddeev algebra vertex models, H.-P. Eckle scaling properties of the Ising model in a field, U. Grimm and B. Nienhuis experimental realizations of integrable reaction-diffusion processes in biological and chemical systems, G.M. Schutz and other papers. (Part contents).
NONLINEAR SYSTEMS AND CLASSICAL IST Introduction Definition of Integrability Lax Pair Technique Inverse Scattering Transform Hamiltonian Structure COORDINATE BETHE ANSATZ Introduction Nonlinear Systems and the CBA Fermionic System Boundary Condition in Bethe Ansatz Heisenberg Spin Chain Spin of the Bethe Ansatz State Other Integrable Models YANG-BAXTER EQUATION Introduction General Description Factorized Scattering Baxter's Star Triangle Relation Vertex Models Reflection Equation Algebra CONTINUOUS INTEGRABLE SYSTEMS Introduction Quantum Continuous Integrable Systems Conserved Quantities Nonultralocal systems and the YBE Operator Product Expansion and YBE Finite Boundary Conditions Modified Classical Yang-Baxter Equation ALGEBRAIC BETHE ANSATZ Introduction Discrete Self Trapping Model Asymmetric XXZ Model in a Magnetic Field Analytical Bethe Ansatz Off-Shell Bethe Ansatz Nested Bethe Ansatz Fusion Procedure Fusion Procedure for Open chains Fusion Procedure for Transfer Matrices Application of Fusion Procedure INTEGRABLE LONG-RANGE MODELS Introduction Long-Range Models from the ABA Symmetry Transformation Calogero-Moser Models SEPARATION OF VARIABLES Introduction Hamilton-Jacobi Equation Sklyanin's Method for SoV Goryachev-Chaplygin Top Quantum Case and the Role of Lie Algebra Bi-Hamiltonian Structure and SoV SoV for GCM Model SoV and Boundary Conditions BACKLUND TRANSFORMATIONS Introduction Permutability Theorem Backlund Transformations and Classical Inverse Scattering Backlund Transformations from Riccati Equation Darboux Backlund Transformations The Exponential Lattice Canonical Transformations Group Property of Backlund Transformations Recent Developments in Backlund Transformation Theory Sklyanin's Formalism for Canonical Backlund Transformations Extended Phase Space Method Quantization of Backlund Transformations Method of Projection Operators QUANTUM GLM EQUATION Introduction Quantum GLM Equation Quantum Floquet Function Exact Quantization Quantum GLM Equation in a Continuous System Bound States and an Alternative Approach APPENDICES Direct Product Calculus Grassman Algebra Bethe Ansatz Equation AKNS Problem BIBLIOGRAPHY INDEX
We propose an expression for the current form of the lowering operator of the sl 2 loop algebra symmetry of the six-vertex model (XXZ spin chain) at roots of unity. This operator has poles which correspond to the evaluation parameters of representation theory which are given as the roots of the Drinfeld polynomial. We explicitly compute these polynomials in terms of the Bethe roots which characterize the highest weight states for all values of S z . From these polynomials we find that the Bethe roots satisfy sum rules for each value of S z .
Manifestly gauge invariant exact renormalization groups by S. Arnone, T. R. Morris, and O. J. Rosten SLE(8/3) and Brownian excursions in annuli by R. O. Bauer Cardy's formula on the triangular lattice, the easy way by V Beffara Rota-Baxter algebras in renormalization of perturbative quantum field theory by K. Ebrahimi-Fard and L. Guo Practicalities of renormalizing quantum field theories by J. A. Gracey Quantum field theory in curved spacetime by S. Hollands Entropy of XYXYXY spin chain and block Toeplitz determinants by A. R. Its, B.-Q. Jin, and V. E. Korepin On the quantitative boundary behavior of SLE by N.-G. Kang The configurational measure on mutually avoiding SLE paths by M. J. Kozdron and G. F. Lawler Dyson-Schwinger equations: From Hopf algebra to number theory by D. Kreimer Two-sided SLE8/3SLE_{8/3}SLE8/3​ and the infinite self-avoiding polygon by G. F. Lawler and J. R. Lind Using the renormalization gorup by D. G. C. McKeon Short distance behavior of scaling functions for the planar ising model by J. Palmer Constructing conformal field theory models by I. Todorov The art of computing loop integrals by S. Weinzierl The transition temperature of the weakly interacting Bose gas by J. Zinn-Justin.