New gapped quantum phases for S=1 spin chain with D2h symmetry

TL;DR

This paper identifies four novel symmetry-protected topological phases in S=1 spin chains with D2h symmetry, expanding the understanding of quantum phases beyond the well-known Haldane phase.

Contribution

The study introduces four new SPT phases in S=1 spin chains with D2h symmetry, constructed from projective representations, and distinguishes them experimentally via end state responses.

Findings

Identified four non-trivial SPT phases with D2h symmetry in S=1 chains.

All phases exhibit gapped bulk, doubly-degenerate end states, and entanglement spectrum.

One phase corresponds to the Haldane phase; three are newly discovered.

Abstract

We study different quantum phases in integer spin systems with on-site D2h=D2xZ2 and translation symmetry. We find four distinct non-trivial phases in S=1 spin chains despite they all have the same symmetry. All the four phases have gapped bulk excitations, doubly-degenerate end states and the doubly-degenerate entanglement spectrum. These non-trivial phases are examples of symmetry protected topological (SPT) phases introduced by Gu and Wen. One of the SPT phase correspond to the Haldane phase and the other three are new. These four SPT phases can be distinguished experimentally by their different response of the end states to weak external magnetic fields. According to Chen-Gu-Wen classification, the D2h symmetric spin chain can have totally 64 SPT phases that do not break any symmetry. Here we constructed seven nontrivial phases from the seven classes of nontrivial projective representations of D2h group. Four of these are found in S=1 spin chains and studied in this paper, and the other three may be realized in S=1 spin ladders or S=2 models.