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Modified rational six vertex model on the rectangular lattice

S. Belliard, R. A. Pimenta, N. A. Slavnov

Abstract

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 Izergin determinant. The proofs are based on the quantum inverse scattering method and its representation theory together with elementary linear algebra.

Modified rational six vertex model on the rectangular lattice

Abstract

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 Izergin determinant. The proofs are based on the quantum inverse scattering method and its representation theory together with elementary linear algebra.
Paper Structure (9 sections, 4 theorems, 109 equations, 7 figures)

This paper contains 9 sections, 4 theorems, 109 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Partition function and quantum groups
  3. R-matrix and Yang-Baxter equation
  4. Operator formalism and quantum group
  5. Rational six vertex model case: auxiliary operators and triangular representation theory
  6. Linear system and modified Izergin determinant formula
  7. Conclusion
  8. Basics about the Yangian $Y(gl_2)$
  9. Modified Izergin determinant

Key Result

Theorem 4.1

Figures (7)

  • Figure 1: Inhomogeneous vertex model on the $m \times n$ rectangular lattice.
  • Figure 2: Graphical picture of a vertex and the R-matrix.
  • Figure 3: Single row monodromy matrix (left) and single column monodromy matrix (right).
  • Figure 4: Modified operators $B(u)$ (left) and $\hat{B}(v)$ (right). The twists are represented by the filled squares.
  • Figure 5: Partition function in different geometries according to the nature of the twist.
  • ...and 2 more figures

Theorems & Definitions (6)

  • Theorem 4.1
  • Theorem A.1
  • proof
  • Definition B.1
  • Proposition B.1
  • Proposition B.2