On Hamiltonians for six-vertex models

TL;DR

This paper establishes a connection between free-fermionic six-vertex models and Hamiltonians, providing determinant formulas for their partition functions, thus advancing understanding of integrable models and their algebraic structures.

Contribution

It introduces Hamiltonians for generalized six-vertex models that recover Boltzmann weights and derives determinant formulas for their partition functions.

Findings

Hamiltonians recover Boltzmann weights of the models.

Partition functions expressed as determinants similar to Jacobi-Trudi identities.

Generalization of previous models with new combinatorial and algebraic insights.

Abstract

In this paper, we explain a connection between a family of free-fermionic six-vertex models and a discrete time evolution operator on one-dimensional Fermionic Fock space. The family of ice models generalize those with domain wall boundary, and we focus on two sets of Boltzmann weights whose partition functions were previously shown to generalize a generating function identity of Tokuyama. We produce associated Hamiltonians that recover these Boltzmann weights, and furthermore calculate the partition functions using commutation relations and elementary combinatorics. We give an expression for these partition functions as determinants, akin to the Jacobi-Trudi identity for Schur polynomials.