# A direct proof of dimerization in a family of SU(n)-invariant quantum spin chains

## TL;DR

This paper provides a rigorous proof of dimerization in a class of SU(n)-invariant quantum spin chains with large spin values, using a novel random loop representation and classical statistical mechanics methods.

## Contribution

It introduces a new proof technique for dimerization in quantum spin chains, applicable to all sufficiently large spins, expanding understanding of quantum phase behavior.

## Key findings

- Dimerization occurs in the studied spin chains for large S.
- The proof employs a random loop representation of the partition function.
- Classical statistical mechanics techniques are effectively applied to quantum models.

## Abstract

We study the family of spin-S quantum spin chains with a nearest neighbor interaction given by the negative of the singlet projection operator. Using a random loop representation of the partition function in the limit of zero temperature and standard techniques of classical statistical mechanics, we prove dimerization for all sufficiently large values of S.