Abundance of hard-hexagon crystals in the quantum pyrochlore antiferromagnet

Abstract

We propose a simple family of valence-bond crystals as potential ground states of the $S=1/2$ and $S=1$ Heisenberg antiferromagnet on the pyrochlore lattice. Exponentially numerous in the linear size of the system, these can be visualized as hard-hexagon coverings, with each hexagon representing a resonating valence-bond ring. This ensemble spontaneously breaks rotation, inversion and translation symmetries. A simple, yet accurate, variational wavefunction allows a precise determination of the energy, confirmed by DMRG and numerical linked cluster expansion, and extended by an analysis of excited states. The identification of the origin of the stability indicates applicability to a broad class of frustrated lattices, which we demonstrate for the checkerboard and ruby lattices. Our work suggests a perspective on such quantum magnets, in which unfrustrated motifs are effectively uncoupled by the frustration of their interactions.

arXiv comment6 pages, 4 papers, 13 pages supplementary material

References in corpus (58)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• The ITensor Software Library for Tensor Network Calculations
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Emergent excitations in a geometrically frustrated magnet
• Gapless spin-liquid ground state in the $S=1/2$ kagome antiferromagnet
• Studying Two Dimensional Systems With the Density Matrix Renormalization Group
• Pyrochlore Antiferromagnet: A Three-Dimensional Quantum Spin Liquid
• First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice
• Gapless spin-liquid phase in the kagome spin-1/2 Heisenberg antiferromagnet
• Finite Temperature Density Matrix Renormalization using an enlarged Hilbert space
• Properties of an algebraic spin liquid on the kagome lattice
• Topological quantum matter with cold atoms
• Spin liquid nature in the Heisenberg $J_1$-$J_2$ triangular antiferromagnet
• Spin liquid phase of the $S=\frac{1}{2}$ $J_1-J_2$ Heisenberg model on the triangular lattice
• Order by distortion and string modes in pyrochlore antiferromagnet
• Ground State of the Kagome Lattice Heisenberg Antiferromagnet
• Signatures of Dirac cones in a DMRG study of the Kagome Heisenberg model
• Competing Spin Liquid States in the Spin-$1/2$ Heisenberg Model On Triangular Lattice
• Generic quantum spin ice
• Time Dependent Variational Principle with Ancillary Krylov Subspace
• Gapless spin liquids on the three dimensional hyper-kagome lattice of Na${}_4$Ir${}_3$O${}_8$
• Dy2Ti2O7 Spin Ice: a Test Case for Emergent Clusters in a Frustrated Magnet
• Possible Quantum Spin Liquid States on the Triangular and Kagome Lattices
• Is the Yb2Ti2O7 pyrochlore a quantum spin ice?
• Singlet Excitations in Pyrochlore: A Study of Quantum Frustration
• A Short Introduction to Numerical Linked-Cluster Expansions
• The $S=1/2$ Kagome Heisenberg Antiferromagnet Revisited
• Magnetism of the N=42 kagome lattice antiferromagnet
• Topological spin liquid on the hyper-kagome lattice of Na_4Ir_3O_8
• Spinons in more than one dimension: Resonance Valence Bond state stabilized by frustration
• Quantum and Classical Phases of the Pyrochlore Heisenberg Model with Competing Interactions
• Antiferromagnetic Quantum Spins on the Pyrochlore Lattice
• Dynamical structure factor of the three-dimensional quantum spin liquid candidate NaCaNi${}_2$F${}_7$
• Absent pinch points and emergent clusters: further neighbour interactions in the pyrochlore Heisenberg antiferromagnet
• Effective Quantum Dimer Model for the Kagome Heisenberg Antiferromagnet: Nearby Quantum Critical Point and Hidden Degeneracy
• The pyrochlore S=1/2 Heisenberg antiferromagnet at finite temperature
• From Spin Glass to Quantum Spin Liquid Ground States in Molybdate Pyrochlores
• Possible inversion symmetry breaking in the $S=1/2$ pyrochlore Heisenberg magnet
• Planar pyrochlore: a strong-coupling analysis
• Monopole Flux State on the Pyrochlore Lattice
• Quantum spin ice with frustrated transverse exchange: from pi-flux phase to nematic quantum spin liquid
• The frustrated Heisenberg antiferromagnet on the checkerboard lattice: the $J_1$--$J_2$ model
• Green's function approach to the magnetic properties of the kagome antiferromagnet
• Symmetry Breaking on the Three-Dimensional Hyperkagome Lattice of Na_4Ir_3O_8
• The s=1/2 Heisenberg Antiferromagnet on the Triangular Lattice: Exact Results and Spin-Wave Theory for Finite Cells
• 1-Dimensional behavior and sliding Luttinger liquid phase in a frustrated spin-1/2 crossed chain model: contribution of exact diagonalizations
• Chiral spin states in the pyrochlore Heisenberg magnet: Fermionic mean-field theory and variational Monte Carlo calculations
• Dimerization tendencies of the pyrochlore Heisenberg antiferromagnet: A functional renormalization group perspective
• Multiboson spin-wave theory for Ba2CoGe2O7, a spin-3/2 easy-plane Neel antiferromagnet with strong single-ion anisotropy
• Corrections to Pauling residual entropy and single tetrahedron based approximations for the pyrochlore lattice Ising antiferromagnet
• Thermodynamics and phase transitions for the Heisenberg model on the pinwheel distorted kagome lattice
• Enhanced symmetry-breaking tendencies in the $S=1$ pyrochlore antiferromagnet
• Tensor network simulation of phase diagram of frustrated J1-J2 Heisenberg model on a checkerboard lattice
• Magnetization process and ordering of the $S=1/2$ pyrochlore magnet in a field

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• Phase diagram of the antiferromagnetic $J_1$-$J_2$ spin-$1$ pyrochlore Heisenberg model
• Quantum Spin Liquids Stabilized by Disorder in Non-Kramers Pyrochlores
• Thermodynamics of the Heisenberg antiferromagnet on the maple-leaf lattice
• Classification and correlation signatures of chiral spin liquids on the pyrochlore lattice
• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice
• Simplex Crystal Ground State and Magnetization Plateaus in the Spin-$1/2$ Heisenberg Model on the Ruby Lattice