Proposal of a spin-one chain model with competing dimer and trimer interactions

TL;DR

This paper introduces a novel spin-1 chain model with competing dimer and trimer interactions, revealing diverse phases including gapped, gapless, topological, and degenerate ground states, driven by the competition between singlet formations.

Contribution

The paper proposes a new spin-1 chain Hamiltonian with competing dimer and trimer interactions, expanding understanding of phase diversity beyond traditional models.

Findings

Identification of multiple phases including gapped, gapless, and topological.

Existence of a symmetry-protected topological phase not derived from standard models.

Ground state degeneracy in one of the phases.

Abstract

A new kind of spin-1 chain Hamiltonian consisting of competing dimer and trimer projection operators is proposed. As the relative strengths and signs of the interactions are varied, the model exhibits a number of different phases including the gapped dimer phase and the gapless trimer phase with critical correlations described by a conformal field theory with central charge $c=2$. A symmetry-protected topological phase also exists in this model, even though the microscopic interactions are not the simple adiabatic extensions of the well-known Heisenberg and the Affleck-Kennedy-Lieb-Tasaki model and contains both two- and three-particle permutations. A fourth phase is characterized by macroscopically degenerate ground states. While bearing almost a one-to-one resemblance to the phase diagram of the bilinear-biquadratic spin-1 chain Hamiltonian, our model is rooted on very different physical origin, namely the two competing tendencies of spin-1 particles to form singlets through either dimer or trimer formation.