The Haldane gap in the SU(3) [3 0 0] Heisenberg chain

TL;DR

This paper computes the Haldane gap in an SU(3) spin chain using variational matrix product states, revealing the minimal gap, symmetry protected topological order, and excitation spectrum.

Contribution

It introduces a variational SU(3) matrix product state approach to calculate the Haldane gap and analyze topological order in the SU(3) Heisenberg chain.

Findings

Minimal gap Δ/J = 0.0263 at momentum 2π/3

Identification of symmetry protected topological order

Full dispersion relation of elementary excitations

Abstract

We calculate the Haldane gap of the $\mathrm{SU}(3)$ spin $[3~0~0]$ Heisenberg model using variational uniform fully symmetric $\mathrm{SU}(3)$ matrix product states, and find that the minimal gap $\Delta /J = 0.0263 $ is obtained in the $[2~1~0]$ sector at momentum $2\pi/3$. We also discuss the symmetry protected topological order of the ground state, and determine the full dispersion relation of the elementary excitations and the correlation lengths of the system.