The planar pyrochlore antiferromagnet: A large-N analysis

Abstract

We study possible quantum phases of the Heisenberg antiferromagnet on the planar pyrochlore lattice, also known as the checkerboard lattice or the square lattice with crossings. It is assumed that the exchange coupling on the square-lattice-links is not necessarily the same as those along the crossing links. When all the couplings are the same, this model may be regarded as a two dimensional analog of the pyrochlore antiferromagnet. The large-N limit of the Sp($N$) generalized model is considered and the phase diagram is obtained by analyzing the fluctuation effects about the $N\to \infty$ limit. We find a topologically-ordered $Z_2$-spin-liquid phase in a narrow region of the phase diagram as well as the plaquette-ordered and staggered spin-Peierls phases as possible quantum-disordered paramagnetic phases.

Typos corrected, two references added, 7 pages, 7 figures

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Cited by in corpus (23)

• Anisotropic pyrochlores and the global phase diagram of the checkerboard antiferromagnet
• The frustrated Heisenberg antiferromagnet on the checkerboard lattice: the $J_1$--$J_2$ model
• Thermodynamics of the Antiferromagnetic Heisenberg Model on the Checkerboard Lattice
• Tensor network simulation of phase diagram of frustrated J1-J2 Heisenberg model on a checkerboard lattice
• Anharmonic Ground state selection in the pyrochlore antiferromagnet
• Numerical study of magnetization plateaux in the spin-1/2 Heisenberg antiferromagnet on the checkerboard lattice
• Effective Hamiltonians for large-S pyrochlore antiferromagnet
• Semiclassical ordering in the large-N pyrochlore antiferromagnet
• Wither the sliding Luttinger liquid phase in the planar pyrochlore
• One-dimensional spin pyrochlore lattice: exact ground state and elementary excitations
• A frustrated spin-1/2 Heisenberg antiferromagnet on a chevron-square lattice
• Supersolid phases of a doped valence-bond quantum antiferromagnet: Evidence for a coexisting superconducting order parameter
• Phase diagram of J1-J2 transverse field Ising model on the checkerboard lattice: a plaquette-operator approach
• U(1) spin liquids and valence bond solids in a large-N three-dimensional Heisenberg model
• Fractionalized Altermagnets: from neighboring and altermagnetic spin-liquids to spin-symmetric band splitting
• Magnetic Order and Mott Transition on the Checkerboard Lattice
• Ground-state phase structure of the spin-$\frac{1}{2}$ anisotropic planar pyrochlore
• The quantum spin quadrumer
• Flux Hamiltonians, Lie Algebras and Root Lattices With Minuscule Decorations
• Multi-$Q$ magnetic phases from frustration and chiral interactions
• A frustrated spin-1 $J_1$--$J_2$ Heisenberg antiferromagnet: An anisotropic planar pyrochlore model
• Semi-Dirac spin liquids and frustrated quantum magnetism on the trellis lattice
• Simplex Crystal Ground State and Magnetization Plateaus in the Spin-$1/2$ Heisenberg Model on the Ruby Lattice