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

Abstract

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.

Spin-spectral-weight distribution and energy range of the parent compound La 2 CuO 4

“…[2] first showed sufficient details of the spin-wave spectrum to demonstrate that a simple nearest-neighbor Heisenberg model must be supplemented by a number of additional terms, including ring exchanges. These terms arise naturally out of a single band Hubbard model with finite U/t, and several detailed studies showed that the spin-wave data in the available energy window could be successfully described by the Hubbard model using a somewhat smaller value of U/t ∼ 6 − 8 than originally thought appropriate [2][3][4][5]. However, part of the spectral weight was deduced to be outside the energy window.…”

“…This raises the important question of whether the more detailed results can still be described in terms of a simple Hubbard model. Here we address this question using a combination of a number of theoretical and numerical approaches, including, in addition to standard treatments, a new spinon approach for the spin excitations [5,7] and density matrix renormalization group (DMRG) calculations for Hubbard cylinders [8][9][10]. We show that the Hubbard model does describe the new neutron scattering results.…”

“…[5]. The ground-state spin degrees of freedom are described by a full s1 fermion band, which coincides with an antiferromagnetic reduced Brillouin zone.…”

“…The spin S = 1 excited states of momentum k = [π, π] − q − q ′ are generated upon breaking one s1 fermion spinon pair, which leads to the emergence of two holes of momenta q and q ′ in the otherwise full s1 band. The inelastic coherent spin-wave spectrum is generated by processes where q points in the nodal direction and q ′ belongs to the boundary of the s1 band reduced zone [5]. The remaining choices of q and q ′ either generate the inelastic incoherent continuum spectral weight or vanishing weight, respectively.…”

“…The studies of Ref. [5] are limited to the spin-wave spectrum. Here we consider the energy-momentum space domain of all above spin S = 1 excited states, which is represented in Fig.…”