# Boundary Perimeter Bethe Ansatz

## TL;DR

This paper connects the partition function of the six-vertex model with reflecting boundaries to Bethe wave functions of open spin chains, using algebraic and coordinate Bethe ansatz methods for arbitrary Baxter lattices.

## Contribution

It introduces a novel approach to compute the partition function for Baxter lattices with reflecting boundaries via algebraic and coordinate Bethe ansatz techniques.

## Key findings

- Partition function expressed via creation operators on a reference state.
- Partition function represented as a sum over permutations and reflections.
- Establishes a link between Baxter lattice invariants and twisted Yangian symmetry.

## Abstract

We study the partition function of the six-vertex model in the rational limit on arbitrary Baxter lattices with reflecting boundary. Every such lattice is interpreted as an invariant of the twisted Yangian. This identification allows us to relate the partition function of the vertex model to the Bethe wave function of an open spin chain. We obtain the partition function in terms of creation operators on a reference state from the algebraic Bethe ansatz and as a sum of permutations and reflections from the coordinate Bethe ansatz.