Ground-state phases of the spin-1 $J_{1}$--$J_{2}$ Heisenberg antiferromagnet on the honeycomb lattice

TL;DR

This study investigates the zero-temperature phase diagram of a spin-1 Heisenberg antiferromagnet on the honeycomb lattice, revealing four distinct phases, including two magnetic and two paramagnetic, with evidence for a quantum spin liquid.

Contribution

The paper employs high-order coupled cluster calculations to identify and characterize four quantum phases, including a potential quantum spin liquid, in the frustrated honeycomb lattice model.

Findings

Identifies two magnetic long-range ordered phases: Néel and Néel-II.

Discovers a gapless quantum spin liquid candidate phase.

Finds a gapped lattice nematic phase with valence-bond order.

Abstract

We study the zero-temperature quantum phase diagram of a spin-1 Heisenberg antiferromagnet on the honeycomb lattice with both nearest-neighbor exchange coupling $J_{1}>0$ and frustrating next-nearest-neighbor coupling $J_{2} \equiv \kappa J_{1} > 0$, using the coupled cluster method implemented to high orders of approximation, and based on model states with different forms of classical magnetic order. For each we calculate directly in the bulk thermodynamic limit both ground-state low-energy parameters (including the energy per spin, magnetic order parameter, spin stiffness coefficient, and zero-field uniform transverse magnetic susceptibility) and their generalized susceptibilities to various forms of valence-bond crystalline (VBC) order, as well as the energy gap to the lowest-lying spin-triplet excitation. In the range $0 < \kappa < 1$ we find evidence for four distinct phases. Two of these are quasiclassical phases with antiferromagnetic long-range order, one with 2-sublattice N\'{e}el order for $\kappa < \kappa_{c_{1}} = 0.250(5)$, and another with 4-sublattice N\'{e}el-II order for $\kappa > \kappa_{c_{2}} = 0.340(5)$. Two different paramagnetic phases are found to exist in the intermediate region. Over the range $\kappa_{c_{1}} < \kappa < \kappa^{i}_{c} = 0.305(5)$ we find a gapless phase with no discernible magnetic order, which is a strong candidate for being a quantum spin liquid, while over the range $\kappa^{i}_{c} < \kappa < \kappa_{c_{2}}$ we find a gapped phase, which is most likely a lattice nematic with staggered dimer VBC order that breaks the lattice rotational symmetry.