The quantum $J_1$--$J_1^{\prime }$--$J_2$ spin-1 Heisenberg model: Influence of the interchain coupling on the ground-state magnetic ordering in 2D

Abstract

We study the phase diagram of the isotropic $J_1$--$J_1^{\prime }$--$J_2$ 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 Néel and stripe states, as compared with all previous results for the corresponding spin-1/2 case. However, we find a quantum tricritical point at $J_1^{\prime }/J_1\approx 0.66\pm 0.03$, $J_2/J_1\approx 0.35\pm 0.02$, where a line of second-order phase transitions between the quasi-classical Néel and stripe-ordered phases (for $J_1^{\prime }/J_1\lesssim 0.66$) meets a line of first-order phase transitions between the same two states (for $J_1^{\prime }/J_1\gtrsim 0.66$)

6 pages. 3 figures. Minor changes in content

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• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• The J1-J2 model: First order phase transition versus deconfinement of spinons
• Quantum $J_1$--$J_2$ antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering
• Coupled Cluster Treatment of the Shastry-Sutherland Antiferromagnet

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