Journal of Algebra, ISSN 0021-8693, 08/2016, Volume 460, pp. 1 - 25

...–Baxter operators of any weights and twisted Rota–Baxter operators are solutions of the proposed system...

Dendriform algebra | Covariant bialgebra | Yang–Baxter equation | Rota–Baxter system | Rota-Baxter system | Yang-Baxter equation | MATHEMATICS | FROBENIUS ALGEBRAS | Algebra

Dendriform algebra | Covariant bialgebra | Yang–Baxter equation | Rota–Baxter system | Rota-Baxter system | Yang-Baxter equation | MATHEMATICS | FROBENIUS ALGEBRAS | Algebra

Journal Article

Nuclear physics. B, ISSN 0550-3213, 2020, Volume 951, p. 114878

...) extensions of Yang-Baxter maps together with their associated systems of PΔEs, based on the ideas presented in [15...

EQUATIONS | BACKLUND-DARBOUX TRANSFORMATIONS | YANG-BAXTER MAPS | DISCRETE | HIERARCHY | PHYSICS, PARTICLES & FIELDS

EQUATIONS | BACKLUND-DARBOUX TRANSFORMATIONS | YANG-BAXTER MAPS | DISCRETE | HIERARCHY | PHYSICS, PARTICLES & FIELDS

Journal Article

Journal of physics. A, Mathematical and theoretical, ISSN 1751-8121, 2020, Volume 53, Issue 3, p. 035203

Symmetries play important roles in physical systems. We study the symmetries of a Hamiltonian system by investigating the asymmetry of the Hamiltonian with respect to certain algebras...

YANG-BAXTER EQUATION | integrable spin chain | QUANTUM Q-DEFORMATIONS | SUQ,H | ANALOG | PHYSICS, MULTIDISCIPLINARY | SYMPLECTIC-GEOMETRY | SU ALGEBRA | asymmetry degree of Hamiltonian systems | quantum harmonic and deformed harmonic systems | PHYSICS, MATHEMATICAL

YANG-BAXTER EQUATION | integrable spin chain | QUANTUM Q-DEFORMATIONS | SUQ,H | ANALOG | PHYSICS, MULTIDISCIPLINARY | SYMPLECTIC-GEOMETRY | SU ALGEBRA | asymmetry degree of Hamiltonian systems | quantum harmonic and deformed harmonic systems | PHYSICS, MATHEMATICAL

Journal Article

Journal of physics. A, Mathematical and theoretical, ISSN 1751-8121, 2018, Volume 51, Issue 38, p. 385203

Integrable discrete scalar equations defined on a 2D or 3D lattice can be rewritten as difference systems in bond variables or in face variables, respectively...

simplex equations | difference substitutions | discrete integrable systems | ALGEBRAS | YANG-BAXTER MAPS | MODELS | PHYSICS, MULTIDISCIPLINARY | EQUATIONS | CLASSIFICATION | PHYSICS, MATHEMATICAL | GEOMETRY | SURFACES | Physics - Exactly Solvable and Integrable Systems

simplex equations | difference substitutions | discrete integrable systems | ALGEBRAS | YANG-BAXTER MAPS | MODELS | PHYSICS, MULTIDISCIPLINARY | EQUATIONS | CLASSIFICATION | PHYSICS, MATHEMATICAL | GEOMETRY | SURFACES | Physics - Exactly Solvable and Integrable Systems

Journal Article

Quantum Information Processing, ISSN 1570-0755, 1/2017, Volume 16, Issue 1, pp. 1 - 9

...–Baxter system and analyze their connections with quantum phase transition. The Yang–Baxter system was perturbed by a twist of $$ e^{i\varphi } $$ e i φ...

Quantum Computing | Data Structures, Cryptology and Information Theory | Quantum fidelity | Quantum phase transition | Mathematical Physics | Quantum Information Technology, Spintronics | Quantum Physics | Yang–Baxter system | Physics | STATES | PHYSICS, MULTIDISCIPLINARY | ENTANGLEMENT | TOPOLOGICAL BASIS | BODY PROBLEM | MODEL | PHYSICS, MATHEMATICAL | GATES | CHAIN | DELTA-FUNCTION INTERACTION | Yang-Baxter system | BAXTERIZATION

Quantum Computing | Data Structures, Cryptology and Information Theory | Quantum fidelity | Quantum phase transition | Mathematical Physics | Quantum Information Technology, Spintronics | Quantum Physics | Yang–Baxter system | Physics | STATES | PHYSICS, MULTIDISCIPLINARY | ENTANGLEMENT | TOPOLOGICAL BASIS | BODY PROBLEM | MODEL | PHYSICS, MATHEMATICAL | GATES | CHAIN | DELTA-FUNCTION INTERACTION | Yang-Baxter system | BAXTERIZATION

Journal Article

Nuclear Physics, Section B, ISSN 0550-3213, 2011, Volume 844, Issue 1, pp. 129 - 145

We study an exactly solvable model of D ( D 3 ) non-Abelian anyons on a one-dimensional lattice with a free coupling parameter in the Hamiltonian. For certain...

Bethe ansatz | Yang–Baxter equation | Drinfeld double | Yang-Baxter equation | ENERGY | POTTS | QUANTUM COMPUTATION | CHAINS | MODEL | TRIANGLE RELATIONS | PHYSICS, PARTICLES & FIELDS

Bethe ansatz | Yang–Baxter equation | Drinfeld double | Yang-Baxter equation | ENERGY | POTTS | QUANTUM COMPUTATION | CHAINS | MODEL | TRIANGLE RELATIONS | PHYSICS, PARTICLES & FIELDS

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 06/2017, Volume 58, Issue 6

Admissible structure constants related to the dual Lie superalgebras of particular Lie superalgebra (C-3 + A) are found by straightforward calculations from...

YANG-BAXTER EQUATION | CLASSIFICATION | ALGEBRAS | QUANTIZATION | PHYSICS, MATHEMATICAL | BIALGEBRAS

YANG-BAXTER EQUATION | CLASSIFICATION | ALGEBRAS | QUANTIZATION | PHYSICS, MATHEMATICAL | BIALGEBRAS

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 9/2017, Volume 2017, Issue 9, pp. 1 - 34

We present an approach to evaluate the full operatorial Q-system of all u p , q | r + s $$ \mathfrak{u}\left(p,q\Big|r+s\right) $$ -invariant spin chains with representations of Jordan-Schwinger type...

Lattice Integrable Models | Quantum Groups | Supersymmetric Gauge Theory | Quantum Physics | Bethe Ansatz | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | YANG-BAXTER EQUATION | REPRESENTATIONS | R-MATRIX | ADS/CFT INTEGRABILITY | BETHE-ANSATZ | QUANTUM INTEGRABLE MODELS | HIDDEN GRASSMANN STRUCTURE | CONFORMAL FIELD-THEORY | MILLS THEORY | XXZ MODEL | PHYSICS, PARTICLES & FIELDS | Operators (mathematics) | Chains | Representations | Mathematical analysis | Yang-Mills theory | Sums

Lattice Integrable Models | Quantum Groups | Supersymmetric Gauge Theory | Quantum Physics | Bethe Ansatz | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | YANG-BAXTER EQUATION | REPRESENTATIONS | R-MATRIX | ADS/CFT INTEGRABILITY | BETHE-ANSATZ | QUANTUM INTEGRABLE MODELS | HIDDEN GRASSMANN STRUCTURE | CONFORMAL FIELD-THEORY | MILLS THEORY | XXZ MODEL | PHYSICS, PARTICLES & FIELDS | Operators (mathematics) | Chains | Representations | Mathematical analysis | Yang-Mills theory | Sums

Journal Article

Annals of Physics, ISSN 0003-4916, 2008, Volume 323, Issue 10, pp. 2614 - 2623

...–Baxter systems.

Quantum criticality | Berry phase | Yang–Baxter systems | Yang-Baxter systems | quantum criticality | S-MATRIX | STATES | DELTA-FUNCTION INTERACTION | PHYSICS, MULTIDISCIPLINARY | ENTANGLEMENT | BODY PROBLEM | BAXTERIZATION | Mathematics | Matrix | Physics | Quantum theory | Physics - Quantum Physics | HAMILTONIANS | SPIN | QUANTUM MECHANICS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | CRITICALITY | R MATRIX

Quantum criticality | Berry phase | Yang–Baxter systems | Yang-Baxter systems | quantum criticality | S-MATRIX | STATES | DELTA-FUNCTION INTERACTION | PHYSICS, MULTIDISCIPLINARY | ENTANGLEMENT | BODY PROBLEM | BAXTERIZATION | Mathematics | Matrix | Physics | Quantum theory | Physics - Quantum Physics | HAMILTONIANS | SPIN | QUANTUM MECHANICS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | CRITICALITY | R MATRIX

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 5/2016, Volume 2016, Issue 5, pp. 1 - 44

.... We show that the theories of this type are connected by spectral dualities, which can be also seen at the level of elliptic Seiberg-Witten integrable systems...

Topological Strings | Brane Dynamics in Gauge Theories | Integrable Hierarchies | String Duality | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | AGT RELATIONS | YANG-BAXTER EQUATION | SUPERSYMMETRIC GAUGE | MATRIX MODELS | MIRROR SYMMETRY | RUIJSENAARS-SCHNEIDER MODEL | INTEGRABLE SYSTEMS | SUSY FIELD-THEORIES | SEIBERG-WITTEN THEORY | CONFORMAL BLOCKS | PHYSICS, PARTICLES & FIELDS | Analysis | Information management | Research institutes | Gauge theory | Amplitudes | Integrals | Chains | Mathematical models | Spectra | Topology | Strings | Physics - High Energy Physics - Theory | High Energy Physics | Symplectic Geometry | Nuclear and High Energy Physics | Theory | Mathematics | High Energy Physics - Theory

Topological Strings | Brane Dynamics in Gauge Theories | Integrable Hierarchies | String Duality | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | AGT RELATIONS | YANG-BAXTER EQUATION | SUPERSYMMETRIC GAUGE | MATRIX MODELS | MIRROR SYMMETRY | RUIJSENAARS-SCHNEIDER MODEL | INTEGRABLE SYSTEMS | SUSY FIELD-THEORIES | SEIBERG-WITTEN THEORY | CONFORMAL BLOCKS | PHYSICS, PARTICLES & FIELDS | Analysis | Information management | Research institutes | Gauge theory | Amplitudes | Integrals | Chains | Mathematical models | Spectra | Topology | Strings | Physics - High Energy Physics - Theory | High Energy Physics | Symplectic Geometry | Nuclear and High Energy Physics | Theory | Mathematics | High Energy Physics - Theory

Journal Article

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, 02/2014, Volume 470, Issue 2162, pp. 20130550 - 20130550

We propose a notion of a pluri-Lagrangian problem, which should be understood as an analogue of multidimensional consistency for variational systems...

Discrete integrable systems | Variational systems | Multi-Dimensional consistency | Discrete forms | Euler-Lagrange equations | YANG-BAXTER EQUATION | discrete forms | MULTIDISCIPLINARY SCIENCES | multi-dimensional consistency | variational systems | FORMULATION | discrete integrable systems | Manifolds | ABS | Mathematical analysis | Consistency | Mathematical models | Corners | Statistical mechanics | Symmetry | 1008 | Euler–Lagrange equations | 120

Discrete integrable systems | Variational systems | Multi-Dimensional consistency | Discrete forms | Euler-Lagrange equations | YANG-BAXTER EQUATION | discrete forms | MULTIDISCIPLINARY SCIENCES | multi-dimensional consistency | variational systems | FORMULATION | discrete integrable systems | Manifolds | ABS | Mathematical analysis | Consistency | Mathematical models | Corners | Statistical mechanics | Symmetry | 1008 | Euler–Lagrange equations | 120

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 2015, Volume 336, Issue 1, pp. 199 - 215

Pluri-Lagrangian systems are variational systems with the multi-dimensional consistency property...

FORMULATION | PHYSICS, MATHEMATICAL | YANG-BAXTER EQUATION

FORMULATION | PHYSICS, MATHEMATICAL | YANG-BAXTER EQUATION

Journal Article

International Journal of Theoretical Physics, ISSN 0020-7748, 3/2017, Volume 56, Issue 3, pp. 643 - 651

.... It is not difficult to find that the Berry phase for this new three-qubit system consistent with the solid angle on the Bloch sphere.

Quantum entanglement | Theoretical, Mathematical and Computational Physics | Berry phase | Quantum Physics | Physics, general | GHZ state | Physics | Elementary Particles, Quantum Field Theory | YANG-BAXTER EQUATION | PHYSICS, MULTIDISCIPLINARY | DIMENSION | QUANTUM GATES

Quantum entanglement | Theoretical, Mathematical and Computational Physics | Berry phase | Quantum Physics | Physics, general | GHZ state | Physics | Elementary Particles, Quantum Field Theory | YANG-BAXTER EQUATION | PHYSICS, MULTIDISCIPLINARY | DIMENSION | QUANTUM GATES

Journal Article

Reviews in Mathematical Physics, ISSN 0129-055X, 07/2019, Volume 31, Issue 6, p. 1930002

.... We show that both approaches provide explicit formulae for M -matrices of the integrable systems in terms of the intertwining matrices...

Lax equations | Many-body integrable systems | IRF-Vertex correspondence | YANG-BAXTER EQUATION | R-MATRIX | C-N | CLEBSCH-GORDAN SERIES | QUANTUM | CALOGERO-MOSER SYSTEMS | PHYSICS, MATHEMATICAL | ELLIPTIC SOLUTIONS | MODULI | SOLVABLE LATTICE MODELS | HOLOMORPHIC BUNDLES

Lax equations | Many-body integrable systems | IRF-Vertex correspondence | YANG-BAXTER EQUATION | R-MATRIX | C-N | CLEBSCH-GORDAN SERIES | QUANTUM | CALOGERO-MOSER SYSTEMS | PHYSICS, MATHEMATICAL | ELLIPTIC SOLUTIONS | MODULI | SOLVABLE LATTICE MODELS | HOLOMORPHIC BUNDLES

Journal Article

Journal of physics. A, Mathematical and theoretical, ISSN 1751-8121, 2018, Volume 51, Issue 31, p. 315202

.... First, we construct the R-matrix-valued Lax pairs for Calogero-Moser models associated with classical root systems...

elliptic integrable systems | Calogero-Moser models | Lax pairs | YANG-BAXTER EQUATION | INTEGRABLE QUANTUM-SYSTEMS | PHYSICS, MULTIDISCIPLINARY | MANY-BODY PROBLEM | SEMISIMPLE LIE-ALGEBRAS | PHYSICS, MATHEMATICAL | SUTHERLAND MODELS | ONE-DIMENSION | PARTICLE-SYSTEMS | HAMILTONIAN-SYSTEMS | HOLOMORPHIC BUNDLES | OPERATORS

elliptic integrable systems | Calogero-Moser models | Lax pairs | YANG-BAXTER EQUATION | INTEGRABLE QUANTUM-SYSTEMS | PHYSICS, MULTIDISCIPLINARY | MANY-BODY PROBLEM | SEMISIMPLE LIE-ALGEBRAS | PHYSICS, MATHEMATICAL | SUTHERLAND MODELS | ONE-DIMENSION | PARTICLE-SYSTEMS | HAMILTONIAN-SYSTEMS | HOLOMORPHIC BUNDLES | OPERATORS

Journal Article

Journal of statistical physics, ISSN 1572-9613, 2013, Volume 150, Issue 4, pp. 704 - 721

We consider the problem of defining quantum integrability in systems with finite number of energy levels starting from commuting matrices and construct new general classes of such matrix models...

Energy level statistic | Physical Chemistry | Integrability | Theoretical, Mathematical and Computational Physics | Dynamical conservation laws | Quantum Physics | Yang Baxter | Statistical Physics, Dynamical Systems and Complexity | Physics | HUBBARD | MODEL | PHYSICS, MATHEMATICAL

Energy level statistic | Physical Chemistry | Integrability | Theoretical, Mathematical and Computational Physics | Dynamical conservation laws | Quantum Physics | Yang Baxter | Statistical Physics, Dynamical Systems and Complexity | Physics | HUBBARD | MODEL | PHYSICS, MATHEMATICAL

Journal Article

理论物理通讯：英文版, ISSN 0253-6102, 2014, Volume 61, Issue 3, pp. 349 - 353

Quantum correlations among parts of a composite quantum system are a fundamental resource for several applications in quantum information...

解析表达式 | 密度矩阵 | 量子比特 | 方程构造 | 量子关联 | 系统部件 | 应用程序 | 和谐 | quantum correlations | quantum discord | Yang-Baxter equation | MATRIX | PHYSICS, MULTIDISCIPLINARY | BERRY PHASE

解析表达式 | 密度矩阵 | 量子比特 | 方程构造 | 量子关联 | 系统部件 | 应用程序 | 和谐 | quantum correlations | quantum discord | Yang-Baxter equation | MATRIX | PHYSICS, MULTIDISCIPLINARY | BERRY PHASE

Journal Article

1989, ISBN 9789810201203, Volume 10., x, 715

Book

Journal of Nonlinear Mathematical Physics: Local and Nonlocal Symmetries in Mathematical Physics. Editors: Norbert Euler and Enrique G. Reyes, ISSN 1402-9251, 12/2017, Volume 24, Issue sup1, pp. 121 - 145

We analyze the relation of the notion of a pluri-Lagrangian system, which recently emerged in the theory of integrable systems, to the classical notion of variational symmetry, due to E. Noether...

pluri-Lagrangian structure | integrable system | Lagrangian system | variational symmetry | Noether theorem | YANG-BAXTER EQUATION | MATHEMATICS, APPLIED | HYDROGEN-ATOM | FORMULATION | PHYSICS, MATHEMATICAL | LATTICE

pluri-Lagrangian structure | integrable system | Lagrangian system | variational symmetry | Noether theorem | YANG-BAXTER EQUATION | MATHEMATICS, APPLIED | HYDROGEN-ATOM | FORMULATION | PHYSICS, MATHEMATICAL | LATTICE

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 11/2016, Volume 12

We present four classes of nonlinear systems which may be considered discrete analogues of the Garnier system...

Integrable systems | Difference equations | Lax pairs | Discrete isomonodromy | 2ND-ORDER | CLASSIFICATION | PHYSICS, MATHEMATICAL | DEFORMATION | difference equations | REDUCTIONS | YANG-BAXTER MAPS | GENERAL-THEORY | discrete isomonodromy | ORDINARY DIFFERENTIAL-EQUATIONS | integrable systems | GEOMETRY

Integrable systems | Difference equations | Lax pairs | Discrete isomonodromy | 2ND-ORDER | CLASSIFICATION | PHYSICS, MATHEMATICAL | DEFORMATION | difference equations | REDUCTIONS | YANG-BAXTER MAPS | GENERAL-THEORY | discrete isomonodromy | ORDINARY DIFFERENTIAL-EQUATIONS | integrable systems | GEOMETRY

Journal Article