The quantum $J_{1}$--$J_{1}'$--$J_{2}$ spin-1 Heisenberg model: Influence of the interchain coupling on the ground-state magnetic ordering in 2D

TL;DR

This study investigates the phase diagram of a spin-1 Heisenberg model on an anisotropic square lattice, revealing a quantum tricritical point and the absence of an intermediate phase, using the coupled cluster method.

Contribution

It provides the first detailed analysis of the spin-1 version of the $J_{1}$--$J_{1}'$--$J_{2}$ model, identifying a quantum tricritical point and clarifying phase transition types.

Findings

No intermediate phase between Néel and stripe states.

Identification of a quantum tricritical point at specific coupling ratios.

Line of second-order transitions meets line of first-order transitions.

Abstract

We study the phase diagram of the isotropic $J_{1}$--$J_{1}'$--$J_{2}$ Heisenberg model for spin-1 particles on an anisotropic square lattice, using the coupled cluster method. We find no evidence for an intermediate phase between the N\'{e}el and stripe states, as compared with all previous results for the corresponding spin-1/2 case. However, we find a quantum tricritical point at $J_{1}'/J_{1} \approx0.66 \pm 0.03$, $J_{2}/J_{1} \approx0.35\pm0.02$, where a line of second-order phase transitions between the quasi-classical N\'{e}el and stripe-ordered phases (for $J_{1}'/J_{1} \lesssim 0.66$) meets a line of first-order phase transitions between the same two states (for $J_{1}'/J_{1} \gtrsim 0.66$)