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The square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions

2009; Elsevier BV; Volume: 824; Issue: 3 Linguagem: Inglês

10.1016/j.nuclphysb.2009.08.014

1873-1562

J. M. P. Carmelo,

Quantum and electron transport phenomena

The momentum bands, energy dispersions, and velocities of the charge c fermions and spin-neutral two-spinon s1 fermions of a square-lattice quantum liquid referring to the Hubbard model on such a lattice of edge length L in the one-and two-electron subspace are studied.The model involves the effective nearest-neighbor integral t and on-site repulsion U and can be experimentally realized in systems of correlated ultra-cold fermionic atoms on an optical lattice and thus our results are of interest for such systems.Our investigations profit from a general rotated-electron description, which is consistent with the model global SO(3)×SO(3)×U (1) symmetry.For the model in the oneand two-electron subspace the discrete momentum values of the c and s1 fermions are good quantum numbers so that in contrast to the original strongly-correlated electronic problem their interactions are residual.The use of our description renders an involved many-electron problem into a quantum liquid with some similarities with a Fermi liquid.For the Hubbard model on a square lattice in the one-and two-electron subspace a composite s1 fermion consists of a spin-singlet spinon pair plus an infinitely thin flux tube attached to it.In the U/4t → ∞ limit of infinite on-site interaction the c fermions become non-interacting spinless fermions and the s1 fermion occupancy configurations that generate the spin degrees of freedom of spin-density m = 0 ground states become within a suitable mean-field approximation for the fictitious magnetic field Bs1 ex 3 brought about by the correlations of the original N electron problem those of a full lowest Landau level with N/2 degenerate one-s1 fermion states of the two-dimensional quantum Hall effect.In turn, for U/4t finite the degeneracy of the N/2 one-s1-fermion states is removed by the emergence of a finite-energy-bandwidth s1 fermion dispersion yet the number of s1 band discrete momentum values remains being given by Bs1 L 2 /Φ0 and the s1 effective lattice spacing by as1 = ls1/ √ 2π where ls1 is the fictitious-magnetic-field length and in our units the fictitious-magnetic-field flux quantum reads Φ0 = 1.Elsewhere it is found that the use of the square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions investigated here contributes to the further understanding of the role of electronic correlations in the unusual properties of the hole-doped cuprate superconductors.This indicates that quantum-Hall-type behavior with or without magnetic field may be ubiquitous in nature.