Symmetry-protected topological phases in the SU(N) Heisenberg spin chain: a Majorana-fermion approach

TL;DR

This paper explores symmetry-protected topological phases in SU(N) Heisenberg spin chains using a Majorana fermion approach, revealing topological protection depends on the parity of N and generalizes previous models.

Contribution

It extends the Majorana fermion method to analyze topological phases in SU(N) spin chains, identifying parity-dependent topological protection for the phases.

Findings

For odd N, the phase lacks topological protection.

For even N, the phase is topologically protected.

The phase belongs to the same class as edge states in self-conjugate antisymmetric representations.

Abstract

The nature of symmetry-protected topological phases of Heisenberg spin chains in totally symmetric representations of rank N of the SU(N) group is investigated through a Majorana fermion study starting from an integrable point. The latter approach generalizes the one pioneered by Tsvelik [A. M. Tsvelik, Phys. Rev. B 42, 10 499 (1990)] to describe the low-energy properties of the Haldane phase of the spin-1 Heisenberg chain from three massive Majorana fermions. We find for all N the emergence of a non-degenerate gapped phase with edge states whose topological protection depends on the parity of N. While for N odd there is no such protection, the phase with even N is shown to be topologically protected. We find that the phase belongs to the same topological class as the phase with edge states living in self-conjugate fully antisymmetric representation of the SU(N) group.