# The valence bond solid in quasicrystals

## TL;DR

This paper introduces a generalized model of Heisenberg quantum antiferromagnets on arbitrary graphs, establishing a unique valence bond solid ground state and developing methods to compute correlation functions using advanced mathematical tools.

## Contribution

It constructs a new generalized model with a unique VBS ground state and links multi point correlators to Young tableaux and Gegenbauer polynomials, expanding analytical techniques.

## Key findings

- Derived explicit expressions for the norm and correlation functions.
- Established a method for computing multi point correlations in 1D models.
- Connected correlation functions with mathematical objects like Young tableaux.

## Abstract

A generalized model of Heisenberg quantum antiferromagnet on an arbitrary graph is constructed so that the VBS is the unique ground state. The norm of the base state and equal time multi point correlation functions are computed in terms of generalized hyper geometric functions. For the one-dimensional periodic Heisenberg model we present a method of computing multi point correlation functions based on the study of a commuting family of transfer matrices. The connection of multi point correlators with Young tableaux and Gegenbauer polynomials is found.