Rigorous results on the ground state of the attractive SU($N$) Hubbard model

Abstract

We study the attractive SU($N$) Hubbard model with particle-hole symmetry. The model is defined on a bipartite lattice with the number of sites $N_A$ $(N_B)$ in the $A$ $(B)$ sublattice. We prove three theorems that allow us to identify the basic ground-state properties: the degeneracy, the fermion number, and the SU($N$) quantum number. We also show that the ground state exhibits charge density wave order when $|N_A-N_B|$ is macroscopically large. The theorems hold for a bipartite lattice in any dimension, even without translation invariance.

arXiv comment14 pages

References in corpus (26)

• A one-dimensional liquid of fermions with tunable spin
• From Nagaoka's ferromagnetism to flat-band ferromagnetism and beyond: An introduction to ferromagnetism in the Hubbard model
• 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
• Collisional stability of a three-component degenerate Fermi gas
• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Degenerate Fermi Gases of Ytterbium
• Precise determination of ${}^6$Li cold collision parameters by radio-frequency spectroscopy on weakly bound molecules
• Realization of SU(2)*SU(6) Fermi System
• Three-body recombination in a three-state Fermi gas with widely tunable interactions
• Color Superfluidity and "Baryon" Formation in Ultracold Fermions
• Degenerate Fermi Gas of ${}^{87}$Sr
• Solving fermion sign problem in quantum Monte Carlo by Majorana representation
• Direct probing of the Mott crossover in the SU($N$) Fermi-Hubbard model
• Hidden symmetry and quantum phases in spin-3/2 cold atomic systems
• Majorana Positivity and the Fermion sign problem of Quantum Monte Carlo Simulations
• Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications
• Trionic phase of ultracold fermions in an optical lattice: A variational study
• Split orthogonal group: A guiding principle for sign-problem-free fermionic simulations
• The ground state of a general electron-phonon Hamiltonian is a spin singlet
• Three-Component Fermi Gas in a one-dimensional Optical Lattice
• Magnetism and domain formation in SU(3)-symmetric multi-species Fermi mixtures
• Reflection Positivity for Majoranas
• Ground State Degeneracy of Interacting Spinless Fermions
• Insulating charge density wave for a half-filled SU(N) Hubbard model with an attractive on-site interaction in one dimension

Cited by in corpus (15)

• Universal description of dissipative Tomonaga-Luttinger liquids with SU($N$) spin symmetry: Exact spectrum and critical exponents
• Cooper quartet correlations in infinite symmetric nuclear matter
• Emergence of Competing Orders and Possible Quantum Spin Liquid in SU(N) Fermions
• Exact eigenstates of multicomponent Hubbard models: SU($N$) magnetic $\eta$ pairing, weak ergodicity breaking, and partial integrability
• Trion states and quantum criticality of attractive SU(3) Dirac fermions
• Charge-4$e$ Superconductivity in a Hubbard model
• Lieb's Theorem and Maximum Entropy Condensates
• Finite Temperature Strong Coupling Expansions for the SU(N) Hubbard Model
• An algebraic approach to revealing magnetic structures of ground states in many-electron systems
• Itinerant ferromagnetism in an SU(3) Fermi-Hubbard model at finite temperatures: A dynamical mean-field theory study
• Ground state properties of the periodic Anderson model with electron-phonon interactions
• Onset of charge incompressibility and Mott gaps in the Honeycomb-Lattice SU(4) Hubbard Model: Lessons for Twisted Bilayer Graphene systems
• Possible condensation of Cooper triples
• $\mathrm{SU}(3)$ Fermi-Hubbard gas with three-body losses: symmetries and dark states
• Generalized Nagaoka ferromagnetism accompanied by flavor-selective Mott states in an SU($N$) Fermi-Hubbard model