Dimers for Type D Relativistic Toda Model

TL;DR

This paper constructs dimer graphs with impurities to model type D relativistic Toda systems, enabling the derivation of Hamiltonians and monodromy matrices through graph folding techniques.

Contribution

It introduces a novel method of folding dimer graphs with impurities to realize type D relativistic Toda models, expanding the graph-based approach to integrable systems.

Findings

Successfully constructs dimer graphs for type D models

Derives Hamiltonian and monodromy matrix from folded graphs

Provides a new graphical framework for relativistic Toda systems

Abstract

We construct dimer graphs for type D relativistic Toda models by introducing impurities to the $Y^{2N,0}$ square dimer graphs. By properly placing the impurities and change of canonical variables assigned to the 1-loops on the dimer graph, we introduce the "folding" of the graphs and get the type D relativistic Toda lattice Hamiltonian and monodromy matrix.