The frustrated spin-$\frac{1}{2}$ $J_1$--$J_2$ isotropic $XY$ model on the honeycomb lattice

Abstract

We study the zero-temperature ground-state (GS) phase diagram of a spin-half $J_1$--$J_2$ $XY$ model on the honeycomb lattice with nearest-neighbor exchange coupling $J_1>0$ and frustrating next-nearest-neighbor exchange coupling $J_2\equiv \kappa J_1>0$, where both bonds are of the isotropic $XY$ type, using the coupled cluster method. Results are presented for the GS energy per spin, magnetic order parameter, and staggered dimer valence-bond crystalline (SDVBC) susceptibility, for values of the frustration parameter in the range $0\le \kappa \le 1$. In this range we find phases exhibiting, respectively, Néel $xy$ planar [N(p)], Néel $z$-aligned [N($z$)], SDVBC, and Néel-II $xy$ planar [N-II(p)] orderings which break the lattice rotational symmetry. The N(p) state, which is stable for the classical version of the model in the range $0\le \kappa \le \frac{1}{6}$, is found to form the GS phase out to a first quantum critical point at ${\kappa }_{c_1}=0.216(5)$, beyond which the stable GS phase has N($z$) order over the range ${\kappa }_{c_1}<\kappa <{\kappa }_{c_2}=0.355(5)$. For values $\kappa >{\kappa }_{c_2}$ we find a strong competition to form the GS phase between states with N-II(p) and SDVBC forms of order. Our best estimate, however, is that the stable GS phase over the range ${\kappa }_{c_2}<\kappa <{\kappa }_{c_3}\approx 0.52(3)$ is a mixed state with both SDVBC and N-II(p) forms of order; and for values $\kappa >{\kappa }_{c_3}$ is the N-II(p) state, which is stable at the classical level only at the highly degenerate point $\kappa =\frac{1}{2}$. Over the range $0\le \kappa \le 1$ we find no evidence for any of the spiral phases that are present classically for all values $\kappa >\frac{1}{6}$, nor for any quantum spin-liquid state.

References in corpus (12)

• Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment
• 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
• 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
• Plaquette valence-bond ordering in J_1-J_2 Heisenberg antiferromagnet on the honeycomb lattice
• 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
• 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
• Complete phase diagram of the spin-1/2 $J_1$-$J_2$-$J_3$ model (with $J_3=J_2$) on the honeycomb lattice
• Quantum phases of hard-core bosons in a frustrated honeycomb lattice
• The ground-state magnetic ordering of the spin-1/2 frustrated J1-J2 XXZ model on the square lattice

Cited by in corpus (11)

• Zigzag antiferromagnetic ground state with anisotropic correlation lengths in the quasi-2D honeycomb lattice compound Na2Co2TeO6
• 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
• Polarized-neutron investigation of magnetic ordering and spin dynamics in BaCo${}_2$(AsO${}_4$)${}_2$ frustrated honeycomb-lattice magnet
• The ground-state phase diagram of the XXZ spin-s kagome antiferromagnet: A coupled-cluster study
• Phase diagram of a frustrated spin-$\frac{1}{2}$ $J_1$--$J_2$ $XXZ$ model on the honeycomb lattice
• Topological spin ordering via Chern-Simons superconductivity
• Quantum phases of the frustrated XY models on the honeycomb lattice
• Ground state and low-temperature magnetism of the quasi-two-dimensional honeycomb compound InCu${}_{2/3}$V${}_{1/3}$O${}_3$
• Possible phases of the spin-$1/2$ $XXZ$ model on a honeycomb lattice by boson-vortex duality
• 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