Dimerization in quantum spin chains with $O(n)$ symmetry

TL;DR

This paper investigates the ground state phases of quantum spin chains with high symmetry, proving dimerization and excitation gaps for large spin values, advancing understanding of quantum phase behavior.

Contribution

It provides a rigorous proof of dimerization and excitation gaps in $O(n)$ symmetric quantum spin chains for sufficiently large spins, which was previously unestablished.

Findings

Dimerization occurs in an open region of the phase diagram.

A spectral gap exists for excitations in the system.

Results are valid for sufficiently large spin $S$.

Abstract

We consider quantum spins with $S\geq1$, and two-body interactions with $O(2S+1)$ symmetry. We discuss the ground state phase diagram of the one-dimensional system. We give a rigorous proof of dimerization for an open region of the phase diagram, for $S$ sufficiently large. We also prove the existence of a gap for excitations.