Exact hole-induced $SU(N)$ flavor-singlets in certain $U=\infty$ $SU(N)$ Hubbard models

Abstract

We prove that the motion of a single hole induces $SU(N)$ flavor-singlets in the $U=\infty$ $SU(N)$ (Fermi) Hubbard model on a Husimi-like tree graph. The result is also generalized to certain $t$-$J$ models with antiferromagnetic interactions and singlet hopping terms typically neglected in the literature. This is an $SU(N)$ generalization of the "counter-Nagaoka theorem" introduced in [Phys. Rev. B 107, L140401 (2023)]. Our results suggest the existence of antiferromagnetic or resonating-valence-bond (RVB)-like polarons in the $t$-$J$ models on a more realistic non-bipartite lattice. Such antiferromagnetic/RVB polarons may be relevant for a novel strong-coupling mechanism of superconductivity or other exotic fractionalized phases of matter.

5 + 1 pages, 4 figures. Exact diagonalization result added

References in corpus (11)

• Theory of Intertwined Orders in High Temperature Superconductors
• Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
• Fractionalized Fermi liquids
• Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism
• Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions
• An SU(N) Mott insulator of an atomic Fermi gas realized by large-spin Pomeranchuk cooling
• Nagaoka states in the SU($n$) Hubbard model
• Trimer states with ${\mathbb{Z}}_3$ topological order in Rydberg atom arrays
• Resonating Valence Bond States with Trimer Motifs
• Exact Hole-induced Resonating-Valence-Bond Ground State in Certain $U=\infty$ Hubbard Models
• Pseudo-spin order of Wigner crystals in multi-valley electron gases

Cited by in corpus (3)

• Kinetic magnetism in the crossover between the square and triangular lattice Fermi-Hubbard models
• Magnetization of electronic ground states in frustrated superstable graphs
• $\mathrm{SU}(3)$ Fermi-Hubbard gas with three-body losses: symmetries and dark states