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Related papers: Fermionic R-Operator for the Fermion Chain Model

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In this paper we review the theory of the Yang-Baxter equation related to the 6-vertex model and its higher spin generalizations. We employ a 3D approach to the problem. Starting with the 3D R-matrix, we consider a two-layer projection of…

Mathematical Physics · Physics 2014-06-11 Vladimir V. Mangazeev

In this paper we discuss a constructive approach to check whether a constant Hamiltonian is Yang-Baxter integrable. We then apply our method to long-range interactions and find the Lax operator and $R$-matrix of the two-loop SU(2) sector in…

High Energy Physics - Theory · Physics 2023-12-20 Marius de Leeuw , Ana. L. Retore

Yang-Baxter R operators symmetric with respect to the orthogonal and symplectic algebras are considered in an uniform way. Explicit forms for the spinorial and metaplectic R operators are obtained. L operators, obeying the RLL relation with…

Mathematical Physics · Physics 2016-02-17 A. P. Isaev , D. Karakhanyan , R. Kirschner

In this paper, we introduce and analyze a new switch operator for the six-vertex model. This operator, derived from the Yang-Baxter equation, allows us to express the partition function with arbitrary boundaries in terms of a base case with…

Combinatorics · Mathematics 2023-03-03 Evelyn Choi , Jadon Geathers , Slava Naprienko

We derive the integral operator form for the general rational solution of the Yang-Baxter equation with $s\ell(2|1)$ symmetry. Considering the defining relations for the kernel of the R-operator as a system of second order differential…

Exactly Solvable and Integrable Systems · Physics 2009-11-07 S. E. Derkachov , D. Karakhanyan , R. Kirschner

We implement the quantum inverse scattering method for the 4-vertex model. In comparison to previous works of the author which examined the 6-vertex, and 20-vertex, models, the 4-vertex model exhibits different characteristics, ranging from…

Mathematical Physics · Physics 2025-06-27 Pete Rigas

For the last fifteen years quantum superalgebras have been used to model supersymmetric quantum systems. A class of quasi-triangular Hopf superalgebras, they each contain a universal $R$-matrix, which automatically satisfies the…

Quantum Algebra · Mathematics 2007-05-23 K. A. Dancer

We find new solutions to the Yang-Baxter equations with the $R$-matrices possessing $sl_q(2)$ symmetry at roots of unity, using indecomposable representations. The corresponding quantum one-dimensional chain models, which can be treated as…

Mathematical Physics · Physics 2011-06-30 D. Karakhanyan , Sh. Khachatryan

We translate between different formulations of Yangian invariants relevant for the computation of tree-level scattering amplitudes in N=4 super-Yang--Mills theory. While the R-operator formulation allows to relate scattering amplitudes to…

High Energy Physics - Theory · Physics 2014-08-27 Johannes Broedel , Marius de Leeuw , Matteo Rosso

The goal of this paper is to study the BMN correspondence in the fermionic sector. On the field theory side, we compute matrix elements of the dilatation operator in N=4 Super Yang-Mills for BMN operators containing two fermion impurities.…

High Energy Physics - Theory · Physics 2009-11-10 George Georgiou , Gabriele Travaglini

The Baxterization process for the dynamical Yang-Baxter equation is studied. We introduce the local dynamical Hecke ,Temperley-Lieb and Birman-Murakami-Wenzl operators, then by inserting spectral parameters, from each representation of…

Representation Theory · Mathematics 2024-01-23 Muze Ren

Baxter's Q-operator is generally believed to be the most powerful tool for the exact diagonalization of integrable models. Curiously, it has hitherto not yet been properly constructed in the simplest such system, the compact spin-1/2…

High Energy Physics - Theory · Physics 2011-03-03 Vladimir V. Bazhanov , Tomasz Lukowski , Carlo Meneghelli , Matthias Staudacher

The composite operator effective potential is compared with the conventional Dyson-Schwinger method as a calculational tool for (2+1)-dimensional quantum electrodynamics. It is found that when the fermion propagator ansatz is put directly…

High Energy Physics - Theory · Physics 2014-11-18 A. Campbell-Smith

The main purpose of this paper is the construction of the R-operator which acts in the tensor product of two infinite-dimensional representations of the conformal algebra and solves Yang-Baxter equation. We build the R-operator as a product…

Mathematical Physics · Physics 2015-06-05 D. Chicherin , S. Derkachov , A. P. Isaev

In this paper we continue our classification of regular solutions of the Yang-Baxter equation using the method based on the spin chain boost operator developed in \cite{deLeeuw:2019zsi}. We provide details on how to find all non-difference…

Mathematical Physics · Physics 2021-11-05 Marius de Leeuw , Chiara Paletta , Anton Pribytok , Ana L. Retore , Paul Ryan

We construct an infinite-dimensional solution of the Yang-Baxter equation (YBE) of rank 1 which is represented as an integral operator with an elliptic hypergeometric kernel acting in the space of functions of two complex variables. This…

Mathematical Physics · Physics 2015-06-05 S. E. Derkachov , V. P. Spiridonov

We construct quantum flux operators with respect to the Poincar\'e symmetry in the massless Dirac theory at future null infinity. An anomalous helicity flux operator emerges from the commutator of the superrotation generators. The helicity…

High Energy Physics - Theory · Physics 2024-12-31 Si-Mao Guo , Wen-Bin Liu , Jiang Long

We consider a class of asymptotic representations of the Borel subalgebra of the quantum affine superalgebra U_q(gl(M|N)^). This is characterized by Drinfeld rational fractions. In particular, we consider contractions of U_q(gl(M|N)) in the…

Mathematical Physics · Physics 2017-07-17 Zengo Tsuboi

The generalization of Lorentz invariance to solvable two-dimensional lattice fermion models has been formulated in terms of Baxter's corner transfer matrix. In these models, the lattice Hamiltonian and boost operator are given by…

High Energy Physics - Lattice · Physics 2009-10-28 H. B. Thacker

We construct Q-operators for the open spin-1/2 XXX Heisenberg spin chain with diagonal boundary matrices. The Q-operators are defined as traces over an infinite-dimensional auxiliary space involving novel types of reflection operators…

Mathematical Physics · Physics 2015-12-09 Rouven Frassek , Istvan M. Szecsenyi