  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.
