Chiral Haldane phases of SU(N) quantum spin chains in the adjoint representation

TL;DR

This paper explores new chiral Haldane phases in SU(N) quantum spin chains, constructing explicit Hamiltonians and analyzing their topological properties, with implications for experimental realization and phase transition understanding.

Contribution

It introduces novel Hamiltonians for chiral AKLT states in SU(N) chains and discusses their physical and topological properties, expanding the understanding of symmetry protected topological phases.

Findings

Construction of explicit Hamiltonians for chiral AKLT states

Identification of N-1 Haldane phases with boundary spins

Connection between gapped and gapless topological phases

Abstract

Gapped quantum spin chains with symmetry PSU(N)=SU(N)/Z(N) are known to possess N distinct symmetry protected topological phases. Besides the trivial phase, there are N-1 Haldane phases which are distinguished by the occurrence of massless boundary spins. Motivated by the potential realization in alkaline-earth atomic Fermi gases, we explicitly construct previously unknown Hamiltonians for two classes of chiral AKLT states and we discuss their physical properties. We also point out a deep connection between symmetry protection in gapped and gapless 1D quantum spin systems and its implications for a potential multicritical nature of topological phase transitions.