Resonating quantum three-coloring wavefunctions for the kagome quantum antiferromagnet

Abstract

Motivated by the recent discovery of a macroscopically degenerate exactly solvable point of the spin-$1/2$ $XXZ$ model for $J_z/J=-1/2$ on the kagome lattice [H. J. Changlani et al. Phys. Rev. Lett 120, 117202 (2018)] -- a result that holds for arbitrary magnetization -- we develop an exact mapping between its exact quantum three-coloring wavefunctions and the characteristic localized and topological magnons. This map, involving resonating two-color loops, is developed to represent exact many-body ground state wavefunctions for special high magnetizations. Using this map we show that these exact ground state solutions are valid for any $J_z/J\ge -1/2$. This demonstrates the equivalence of the ground-state wavefunction of the Ising, Heisenberg and $XY$ regimes all the way to the $J_z/J=-1/2$ point for these high magnetization sectors. In the hardcore bosonic language, this means that a certain class of exact many-body solutions, previously argued to hold for purely repulsive interactions ($J_z\ge 0$), actually hold for attractive interactions as well, up to a critical interaction strength. For the case of zero magnetization, where the ground state is not exactly known, we perform density matrix renormalization group calculations. Based on the calculation of the ground state energy and measurement of order parameters, we provide evidence for a lack of any qualitative change in the ground state on finite clusters in the Ising ($J_z\gg J$), Heisenberg ($J_z=J$) and $XY$ ($J_z=0$) regimes, continuing adiabatically to the vicinity of the macroscopically degenerate $J_z/J=-1/2$ point. These findings offer a framework for recent results in the literature, and also suggest that the $J_z/J=-1/2$ point is an unconventional quantum critical point whose vicinity may contain the key to resolving the spin-$1/2$ kagome problem.

10 pages, 10 figures

References in corpus (10)

• Spin Dynamics of the Spin-1/2 Kagome Lattice Antiferromagnet ZnCu_3(OH)_6Cl_2
• Identifying Topological Order by Entanglement Entropy
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Bose condensation in flat bands
• Exact low-temperature behavior of kagome antiferromagnet at high fields
• Distinct Spin Liquids and their Transitions in Spin-1/2 XXZ Kagome Antiferromagnets
• Twelve sublattice ordered phase in the J1-J2 model on the kagome lattice
• Variational study of J1-J2 Heisenberg model on Kagome lattice using projected Schwinger boson wave functions
• Chern-Simons theory of the magnetization plateaus of the spin-1/2 quantum XXZ Heisenberg model on Kagome Lattice
• Fermionic spin excitations in two and three-dimensional antiferromagnets

Cited by in corpus (17)

• Exact three-colored quantum scars from geometric frustration
• Frustration-induced emergent Hilbert space fragmentation
• Effect of perturbations on the kagome $S=1/2$ antiferromagnet at all temperatures
• Gutzwiller-projected states for the $J_1$-$J_2$ Heisenberg model on the kagome lattice: achievements and pitfalls
• Flat-band physics in the spin-1/2 sawtooth chain
• Motif magnetism and quantum many-body scars
• Colorful points in the XY regime of XXZ quantum magnets
• Competing emergent Potts orders and possible nematic spin liquids in the Kagome $J_1-J_3$ Heisenberg model
• Non-ergodic one-magnon magnetization dynamics of the antiferromagnetic delta chain
• A continuous family of fully-frustrated Heisenberg model on the Kagome lattice
• Exactly solvable spin-1/2 XYZ models with highly-degenerate, partially ordered, ground states
• Anomalous thermodynamics of a quantum spin system with large residual entropy
• Non-perturbative approach to quantum liquid ground states on geometrically frustrated Heisenberg antiferromagnets
• Magneto- and barocaloric properties of the ferro-antiferromagnetic sawtooth chain
• Chemistry of the spin-1/2 kagome Heisenberg antiferromagnet
• Two-dimensional spin models with macroscopic degeneracy
• Permanent oscillations and solitary wave behavior in flatband Heisenberg quantum spin systems