2010/03/31 by J. M. P. Carmelo · 5 citations
Materials Science · Physics and Astronomy · #Advanced Condensed Matter Physics #Antiferromagnetism #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Fermion #Hubbard model #Invariant (physics) #Ising model #Lattice (music) #Mathematical physics #Organic and Molecular Conductors Research #Particle physics #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Quantum number #Quark #Spinon #Spins #Square lattice #Superconductivity #Theoretical physics #Unitary state #Unitary transformation #cond-mat.str-el
paper · pdf · open access · doi:10.1016/j.aop.2011.09.001
published in arXiv (Cornell University) 327(3), 553-638 (Cornell University) · 72 pages, 6 figures, in press in Annals of Physics (2012)
arxiv created 2012/01/28 · openalex publication_date 2012/03/01 · arxiv updated 2013/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper a description of the energy eingenstates of the Hubbard model on the square lattice with nearest-neighbor transfer integral t, on-site repulsion U, and Na2≫ 1 sites in terms of occupancy configurations of charge c fermions, spin-1/2 spinons, and η-spin-1/2 η-spinons is introduced. Such objects emerge from a suitable electron - rotated-electron unitary transformation. In chromodynamics the quarks have color but all quark-composite physical particles are color-neutral. Within our description the η-spinon (and spinons) that are not invariant under the electron - rotated-electron unitary transformation have η spin 1/2 (and spin 1/2) but are part of η-spin-neutral (and spin-neutral) 2ν-η-spinon (and 2ν-spinon) composite ην fermions (and sν fermions). Here ν=1,2,... is the number of η-spinon (and spinon) pairs. In turn, a well-defined number of independent spinons and independent η-spinons are invariant under the electron - rotated-electron unitary transformation. Simple occupancy configurations of (i) the c fermions, (ii) independent spinons and 2ν-spinon composite sν fermions, and (iii) independent η-spinons and 2ν-η-spinon composite ην fermions generate an useful complete set of states. The configurations (i), (ii), and (iii) correspond to the state representations of the U(1), spin SU(2), and η-spin SU(2) symmetries, respectively, associated with the model SO(3)× SO(3)× U(1) =[SU(2)× SU(2)× U(1)]/Z22 global symmetry.