Exact Hole-induced Resonating-Valence-Bond Ground State in Certain $U=\infty$ Hubbard Models

Abstract

We prove that the motion of a single hole induces the nearest-neighbor resonating-valence-bond ground state in the $U=\infty$ Hubbard model on a triangular cactus - a tree-like variant of a kagome lattice. The result can be easily generalized to $t-J$ models with antiferromagnetic interactions $J\ge 0$ on the same graphs. This is a weak converse of Nagaoka's theorem of ferromagnetism on a bipartite lattice.

4 pages + references, a revised version

References in corpus (6)

• Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
• Fractionalized Fermi liquids
• Unifying Kitaev magnets, kagome dimer models and ruby Rydberg spin liquids
• Fermionic spin excitations in two and three-dimensional antiferromagnets
• Interstitial-induced ferromagnetism in a two-dimensional Wigner crystal
• Structure factor of low-energy spin excitations in a S=1/2 kagome antiferromagnet

Cited by in corpus (7)

• Superconducting valence bond fluid in lightly doped 8-leg $t$-$J$ cylinders
• Resonating Valence Bond States in an Electron-Phonon System
• A resonant valence bond spin liquid in the dilute limit of doped frustrated Mott insulators
• Kinetic magnetism in the crossover between the square and triangular lattice Fermi-Hubbard models
• Exact hole-induced $SU(N)$ flavor-singlets in certain $U=\infty$ $SU(N)$ Hubbard models
• Shaping Magnetic Order by Local Frustration for Itinerant Fermions on a Graph
• Magnetization of electronic ground states in frustrated superstable graphs