Planar pyrochlore, quantum ice and sliding ice

Abstract

We study quantum antiferromagnetism on the highly frustrated checkerboard lattice, also known as the square lattice with crossings. The quantum Heisenberg antiferromagnet on this lattice is of interest as a two-dimensional analog of the pyrochlore lattice magnet. By combining several approaches we conclude that this system is most likely ordered for all values of spin, $S$, with a Neel state for large $S$ giving way to a two-fold degenerate valence-bond solid for smaller $S$. We show next that the Ising antiferromagnet with a weak four-spin exchange, equivalent to square ice with the leading quantum dynamics, exhibits long range ``anti-ferroelectric'' order. As a byproduct of this analysis we obtain, in the system of weakly coupled ice planes, a sliding phase with XY symmetry.

5 pages, 2 postscript figures automatically included

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• New physics in frustrated magnets: Spin ices, monopoles, etc
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• Low-Temperature Low-Field Phases of the Pyrochlore Quantum Magnet Tb${}_2$Ti${}_2$O${}_7$
• Correlated Fermions on a Checkerboard Lattice
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• Spin-wave analysis of the transverse-field Ising model on the checkerboard lattice
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• Topologically stable ergodicity breaking from emergent higher-form symmetries in generalized quantum loop models
• Wither the sliding Luttinger liquid phase in the planar pyrochlore
• A frustrated spin-1/2 Heisenberg antiferromagnet on a chevron-square lattice
• Mixed Columnar-Plaquette Crystal of correlated fermions on the 2D pyrochlore lattice at fractional filling
• Quantum phase diagram of two-dimensional transverse field Ising model: unconstrained tree tensor network and mapping analysis
• Phase diagram of J1-J2 transverse field Ising model on the checkerboard lattice: a plaquette-operator approach
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• Quantum order by disorder in a semiclassical spin ice
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• Role of Frustration in a Weakly Disordered Checkerboard Lattice
• Classical fully-packed loop model with attractive interactions on the square lattice
• Strings in strongly correlated electron systems
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• Low-temperature specific heat and heat transport of Tb${}_2$Ti${}_{2-x}$Zr${}_x$O${}_7$ single crystals
• Fractionally charged excitations on frustrated lattices
• Jordan-Wigner composite-fermion liquids in 2D quantum spin-ice
• A frustrated spin-1 $J_1$--$J_2$ Heisenberg antiferromagnet: An anisotropic planar pyrochlore model
• Flux fractionalization transition in anisotropic $S=1$ antiferromagnets and dimer-loop models