Effect of anisotropy on the ground-state magnetic ordering of the spin-half quantum $J_1^{XXZ}$--$J_2^{XXZ}$ model on the square lattice

Abstract

We study the zero-temperature phase diagram of the 2D quantum $J_1^{XXZ}$--$J_2^{XXZ}$ spin-1/2 anisotropic Heisenberg model on the square lattice. In particular, the effects of the anisotropy $\Delta$ on the $z$-aligned Néel and (collinear) stripe states, as well as on the $xy$-planar-aligned Néel and collinear stripe states, are examined. All four of these quasiclassical states are chosen in turn as model states on top of which we systematically include the quantum correlations using a coupled cluster method analysis carried out to very high orders. We find strong evidence for two {\it quantum triple points} (QTP's) at (${\Delta }^c=-0.10\pm 0.15,J_2^c/J_1=0.505\pm 0.015$) and (${\Delta }^c=2.05\pm 0.15,J_2^c/J_1=0.530\pm 0.015$), between which an intermediate magnetically-disordered phase emerges to separate the quasiclassical Néel and stripe collinear phases. Above the upper QTP ($\Delta \gtrsim 2.0$) we find a direct first-order phase transition between the Néel and stripe phases, exactly as for the classical case. The $z$-aligned and $xy$-planar-aligned phases meet precisely at $\Delta =1$, also as for the classical case. For all values of the anisotropy parameter between those of the two QTP's there exists a narrow range of values of $J_2/J_1$, ${\alpha }^{c_1}(\Delta )<J_2/J_1<{\alpha }^{c_2}(\Delta )$, centered near the point of maximum classical frustration, $J_2/J_1=1/2$, for which the intermediate phase exists. This range is widest precisely at the isotropic point, $\Delta =1$, where ${\alpha }^{c_1}(1)=0.44\pm 0.01$ and ${\alpha }^{c_2}(1)=0.59\pm 0.01$. The two QTP's are characterized by values $\Delta ={\Delta }^c$ at which ${\alpha }^{c_1}({\Delta }^c)={\alpha }^{c_2}({\Delta }^c)$.

28 pages, 5 figures

References in corpus (8)

• "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
• The quantum $J_1$-$J_1^{\prime }$-$J_2$ spin-1/2 Heisenberg model: Influence of the interchain coupling on the ground-state magnetic ordering in 2D
• Frustrated Quantum Antiferromagnets: Application of High-Order Coupled Cluster Method
• Ground-state long-range order in quasi-one-dimensional Heisenberg quantum antiferromagnets: High-order coupled-cluster calculations

Cited by in corpus (22)

• Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment
• Quasiclassical magnetic order and its loss in a spin-1/2 Heisenberg antiferromagnet on a triangular lattice with competing bonds
• The spin-1/2 square-lattice J_1-J_2 model: The spin-gap issue
• The frustrated Heisenberg antiferromagnet on the honeycomb lattice: A candidate for deconfined quantum criticality
• The frustrated Heisenberg antiferromagnet on the checkerboard lattice: the $J_1$--$J_2$ model
• The ground-state phase diagram of the XXZ spin-s kagome antiferromagnet: A coupled-cluster study
• Magnetic order on a frustrated spin-1/2 Heisenberg antiferromagnet on the Union Jack lattice
• Spin-1/2 Heisenberg antiferromagnet on an anisotropic kagome lattice
• The frustrated spin-$\frac{1}{2}$ $J_1$--$J_2$ isotropic $XY$ model on the honeycomb lattice
• High-Order Coupled Cluster Method (CCM) Calculations for Quantum Magnets with Valence-Bond Ground States
• Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on a square-lattice bilayer: High-order study of the quantum critical behavior of the $J_1$--$J_2$--$J_1^{\perp }$ model
• Phase diagram of a frustrated spin-$\frac{1}{2}$ $J_1$--$J_2$ $XXZ$ model on the honeycomb lattice
• Emergence of string-valence bond solid state in the frustrated $J_1-J_2$ transverse field Ising model on the square lattice
• The Coupled Cluster Method Applied to Quantum Magnets: A New LPSUB$m$ Approximation Scheme for Lattice Models
• A frustrated quantum spin-${\boldmath s}$ model on the Union Jack lattice with spins ${\boldmath s>1/2}$
• Spin-$S$ Kitaev-Heisenberg model on the honeycomb lattice: A high-order treatment via the many-body coupled cluster method
• The Spin-Half {\it XXZ} Antiferromagnet on the Square Lattice Revisited: A High-Order Coupled Cluster Treatment
• The ground-state magnetic ordering of the spin-1/2 frustrated J1-J2 XXZ model on the square lattice
• Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on an $AA$-stacked honeycomb bilayer: High-order study of the collinear magnetic phases of the $J_1$--$J_2$--$J_1^{\perp }$ model
• End-point singularity of the $XY$-paramagnetic phase boundary for the $(2+1)$D $S=1$ square-lattice $J_1$-$J_2$ $XY$ model with the single-ion anisotropy
• $XY$-VBS phase boundary for the square-lattice $J_1$-$J_2$ $XXZ$ model with the ring exchange
• Crystal field splittings and magnetic ground state of the square-lattice antiferromagnets YbBi2ClO4 and YbBi2IO4 with Jeff = 1/2