Heisenberg model and Rigged Configurations

TL;DR

This paper establishes a correspondence between solutions of the spin-1/2 isotropic Heisenberg model for N=12 and rigged configurations, using Takahashi quantum numbers and riggings comparison.

Contribution

It introduces a novel correspondence linking solutions of the Heisenberg model to rigged configurations through quantum numbers comparison.

Findings

All solutions for N=12 are mapped to rigged configurations.

The correspondence is based on lexicographical comparison of quantum numbers and riggings.

Provides a new combinatorial perspective on the Heisenberg model solutions.

Abstract

We show a correspondence of all the solutions of the spin-1/2 isotropic Heisenberg model for N=12 to the rigged configurations based on the comparison of the set of Takahashi quantum numbers in lexicographical order with the set of riggings of the rigged configurations in co-lexicographical order.