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Related papers: Variations on Slavnov's scalar product

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We compute scalar products of off-shell Bethe vectors in models with $o_{2n+1}$ symmetry. The scalar products are expressed as a sum over partitions of the Bethe parameter sets, the building blocks being the so-called highest coefficients.…

Mathematical Physics · Physics 2025-07-23 A. Liashyk , S. Pakuliak , E. Ragoucy

We revisit the quantum/classical integrable model correspondence in the context of inhomogeneous finite length XXZ spin-1/2 chains with periodic boundary conditions and show that the Bethe scalar product of an arbitrary state and a Bethe…

Mathematical Physics · Physics 2017-08-23 O. Foda , G. Schrader

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 continue the work of Belliard, Pimenta and Slavnov (2024) studying the modified rational six vertex model. We find another formula of the partition function for the inhomogeneous model, in terms of a determinant that mix the modified…

Mathematical Physics · Physics 2026-03-11 Matthieu Cornillault , Samuel Belliard

We compute the partition function of the trigonometric SOS model with one reflecting end and domain wall type boundary conditions. We show that in this case, instead of a sum of determinants obtained by Rosengren for the SOS model on a…

Mathematical Physics · Physics 2014-11-20 Ghali Filali , Nikolai Kitanine

Based on the results obtained in [Hucht, J. Phys. A: Math. Theor. 50, 065201 (2017)], we show that the partition function of the anisotropic square lattice Ising model on the $L \times M$ rectangle, with open boundary conditions in both…

Mathematical Physics · Physics 2021-09-29 Alfred Hucht

We calculate the scalar product of Bethe states of the XXZ spin-$\frac{1}{2}$ chain with general integrable boundary conditions. The off-shell equations satisfied by the transfer matrix and the off-shell Bethe vectors allow one to derive a…

Mathematical Physics · Physics 2021-09-01 Samuel Belliard , Rodrigo A. Pimenta , Nikita A. Slavnov

We consider the homogeneous five-vertex model on a rectangle domain of the square lattice with so-called scalar-product boundary conditions. Peculiarity of these boundary conditions is that the configurations of the model are in an…

Mathematical Physics · Physics 2024-06-12 Ivan N. Burenev , Andrei G. Pronko

Fully inhomogeneous spin Hall-Littlewood symmetric rational functions $\mathsf{F}_\lambda$ arise in the context of $\mathfrak{sl}(2)$ higher spin six vertex models, and are multiparameter deformations of the classical Hall-Littlewood…

Combinatorics · Mathematics 2021-07-23 Leonid Petrov

We study the inner product of two Bethe states, one of which is taken on-shell, in an inhomogeneous XXX chain in the Sutherland limit, where the number of magnons is comparable with the length L of the chain and the magnon rapidities…

High Energy Physics - Theory · Physics 2015-06-18 Eldad Bettelheim , Ivan Kostov

In the paper, we consider the extended Gross-Witten-Wadia unitary matrix model by introducing a logarithmic term in the potential. The partition function of the model can be expressed equivalently in terms of the Toeplitz determinant with…

Mathematical Physics · Physics 2024-02-20 Yu Chen , Shuai-Xia Xu , Yu-Qiu Zhao

A natural first step in the classification of all `physical' modular invariant partition functions $\sum N_{LR}\,\c_L\,\C_R$ lies in understanding the commutant of the modular matrices $S$ and $T$. We begin this paper extending the work of…

High Energy Physics - Theory · Physics 2009-10-22 Terry Gannon

The trigonometric six-vertex model with domain wall boundary conditions and one partially reflecting end on a lattice of size $2n\times m$, $m\leq n$, is considered. The partition function is computed using the Izergin-Korepin method,…

Mathematical Physics · Physics 2022-05-04 Linnea Hietala

The antiperiodic transfer matrix associated to higher spin representations of the rational 6-vertex Yang-Baxter algebra is analyzed by generalizing the approach introduced recently in [1], for the cyclic representations, in [2], for the…

Mathematical Physics · Physics 2013-06-04 G. Niccoli

We consider a rational six vertex model on a rectangular lattice with boundary conditions that generalize the usual domain wall type. We find that the partition function of the inhomogeneous version of this model is given by a modified…

Mathematical Physics · Physics 2024-01-10 S. Belliard , R. A. Pimenta , N. A. Slavnov

We describe fundamental equations which define the topological ground states in the lattice realization of the SU(2) BF phase. We introduce a new scalar Hamiltonian, based on recent works in quantum gravity and topological models, which is…

General Relativity and Quantum Cosmology · Physics 2012-08-27 Valentin Bonzom , Etera R. Livine

Our work deals with symmetric rational functions and probabilistic models based on the fully inhomogeneous six vertex (ice type) model satisfying the free fermion condition. Two families of symmetric rational functions $F_\lambda,G_\lambda$…

Probability · Mathematics 2023-01-30 Amol Aggarwal , Alexei Borodin , Leonid Petrov , Michael Wheeler

We study three-point functions of single-trace operators in the su(1|1) sector of planar N = 4 SYM borrowing several tools based on Integrability. In the most general configuration of operators in this sector, we have found a determinant…

High Energy Physics - Theory · Physics 2016-09-21 Joao Caetano , Thiago Fleury

We study lattice configurations related to S_n, the scalar product of an off-shell state and an on-shell state in rational A_n integrable vertex models, n = {1, 2}. The lattice lines are colourless and oriented. The state variables are n…

Mathematical Physics · Physics 2013-03-19 O. Foda , M. Wheeler

We study the scalar products between Bethe states in the XXZ spin chain with anisotropy $|\Delta|>1$ in the semi-classical limit where the length of the spin chain and the number of magnons tend to infinity with their ratio kept finite and…

High Energy Physics - Theory · Physics 2017-04-05 Yunfeng Jiang , Joren Brunekreef