# Exact diagonalization of $\mathrm{SU}(N)$ Heisenberg and AKLT chains using the full $\mathrm{SU}(N)$ symmetry

## TL;DR

This paper introduces a method for exact diagonalization of $ ext{SU}(N)$ spin chains using Young tableaux, enabling analysis of larger systems and investigation of edge states in $ ext{SU}(N)$ models.

## Contribution

It develops a generalized scheme for exact diagonalization of $ ext{SU}(N)$ chains using Young tableaux, improving efficiency and scalability over previous methods.

## Key findings

- Efficient basis construction for $ ext{SU}(N)$ subsectors
- Analysis of edge states in $ ext{SU}(N)$ Heisenberg and AKLT models
- Ability to study larger systems than before

## Abstract

We present a method for the exact diagonalization of the $\mathrm{SU}(N)$ Heisenberg interaction Hamiltonian, using Young tableaux to work directly in each irreducible representation of the global $\mathrm{SU}(N)$ group. This generalized scheme is applicable to chains consisting of several particles per site, with any $\mathrm{SU}(N)$ symmetry at each site. Extending some of the key results of substitutional analysis, we demonstrate how basis states can be efficiently constructed for the relevant $\mathrm{SU}(N)$ subsector, which, especially with increasing values of $N$ or numbers of sites, has a much smaller dimension than the full Hilbert space. This allows us to analyze systems of larger sizes than can be handled by existing techniques. We apply this method to investigate the presence of edge states in $\mathrm{SU}(N)$ Heisenberg and AKLT Hamiltonians.