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Related papers: Switch Operators for the Six-Vertex Model

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The partition function of the six-vertex model on a square lattice with domain wall boundary conditions (DWBC) is rewritten as a hermitean one-matrix model or a discretized version of it (similar to sums over Young diagrams), depending on…

Mathematical Physics · Physics 2009-10-31 P. Zinn-Justin

We consider the enumeration of states in the Brubaker-Bump-Friedberg six-vertex model, whose boundary conditions are determined by an integer partition. In general, we find the number of states is a polynomial in the largest part of the…

We develop an approach for constructing the Baxter Q-operators for generic sl(N) spin chains. The key element of our approach is the possibility to represent a solution of the the Yang Baxter equation in the factorized form. We prove that…

Exactly Solvable and Integrable Systems · Physics 2009-02-12 S. E. Derkachov , A. N. Manashov

This work is based on the author's PhD thesis. The main result of the thesis is the use of the boost operator to develop a systematic method to construct new integrable spin chains with nearest-neighbour interaction and characterized by an…

Statistical Mechanics · Physics 2023-12-04 Chiara Paletta

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

We diagonalize the transfer matrix of the inhomogeneous vertex models of the 6-vertex type in the anti-ferroelectric regime intoducing new types of q-vertex operators. The special cases of those models were used to diagonalize the s-d…

High Energy Physics - Theory · Physics 2009-10-28 Atsushi Nakayashiki

We construct the explicit $Q$-operator incorporated with the $sl_2$-loop-algebra symmetry of the six-vertex model at roots of unity. The functional relations involving the $Q$-operator, the six-vertex transfer matrix and fusion matrices are…

Statistical Mechanics · Physics 2010-01-08 Shi-shyr Roan

Vertical-arrow fluctuations near the boundaries in the six-vertex model on the two-dimensional $N \times N$ square lattice with the domain wall boundary conditions are considered. The one-point correlation function (`boundary polarization')…

Statistical Mechanics · Physics 2009-11-07 N. M. Bogoliubov , A. V. Kitaev , M. B. Zvonarev

Baxter's Q-operator for the quantum transfer matrix of the XXZ spin-chain is constructed employing the representation theory of quantum groups. The spectrum of this Q-operator is discussed and novel functional relations which describe the…

Mathematical Physics · Physics 2007-05-23 Christian Korff

In this paper, we introduce a class of colored stochastic vertex models with U-turn right boundary. The vertex weights in the models satisfy the Yang-Baxter equations and the reflection equation. Based on these equations, we derive…

Probability · Mathematics 2024-01-17 Chenyang Zhong

In this note, we consider the six-vertex model with domain wall boundary conditions, defined on a $M\times M$ lattice, in the inhomogeneous case where the partition function depends on 2M inhomogeneities $\lambda_j$ and $\mu_k$. For a…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 V. Korepin , P. Zinn-Justin

Functional equations methods are a fundamental part of the theory of Exactly Solvable Models in Statistical Mechanics and they are intimately connected with Baxter's concept of commuting transfer matrices. This concept has culminated in the…

Mathematical Physics · Physics 2015-06-18 W. Galleas

The integrability of the one-dimensional (1D) fermion chain model is investigated in the framework of the Quantum Inverse Scattering Method (QISM). We introduce a new R-operator for the fermion chain model, which is expressed in terms of…

High Energy Physics - Theory · Physics 2009-10-31 Yukiko Umeno , Masahiro Shiroishi , Miki Wadati

We present numerical results for the six-vertex model with a variety of boundary conditions. Adapting an algorithm proposed by Allison and Reshetikhin for domain wall boundary conditions, we examine some modifications of these boundary…

Statistical Mechanics · Physics 2018-05-11 Ivar Lyberg , Vladimir Korepin , G. A. P. Ribeiro , Jacopo Viti

We derive determinant expressions for the partition functions of spin-k/2 vertex models on a finite square lattice with domain wall boundary conditions.

Mathematical Physics · Physics 2011-02-16 A Caradoc , O Foda , N Kitanine

We obtain the Baxter Q-operators in the $U_q(\hat{sl}_2)$ invariant integrable models as a special limits of the quantum transfer matrices corresponding to different spins in the auxiliary space both from the functional relations and from…

Mathematical Physics · Physics 2015-06-23 A. A. Ovchinnikov

We show factorization formulas for a class of partition functions of rational six vertex model. First we show factorization formulas for partition functions under triangular boundary. Further, by combining the factorization formulas with…

Mathematical Physics · Physics 2025-01-29 Kohei Motegi

In this work we relate the spectral problem of the toroidal six-vertex model's transfer matrix with the theory of integrable non-linear differential equations. More precisely, we establish an analogy between the Classical Inverse Scattering…

Mathematical Physics · Physics 2018-08-30 W. Galleas

For any algebra two families of coloured Yang-Baxter operators are constructed, thus producing solutions to the two-parameter quantum Yang-Baxter equation. An open problem about a system of functional equations is stated. The matrix forms…

Quantum Algebra · Mathematics 2007-05-23 Florin F. Nichita , Deepak Parashar

In this paper, we construct solvable ice models (six-vertex models) with stochastic weights and U-turn right boundary, which we term ``stochastic symplectic ice''. The models consist of alternating rows of two types of vertices. The…

Mathematical Physics · Physics 2022-06-22 Chenyang Zhong