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Physical review. B, Condensed matter

Jastrow states for highly correlated two-dimensional Hubbard fermions

E. J. Melé

Published Aug 1, 1989• 7 citations
Publisher

Abstract

We discuss a representation of the large-U Hubbard Hamiltonian for fermions on a two-dimensional lattice, in which the Gutzwiller constraint is imposed as a kinematical constraint on the motion of the underlying quasiparticles. At the half-filled band this construction identifies the ``Kalmeyer-Laughlin'' singlet as a unique Jastrow state satisfying the quantum constraints of the large-U problem. Away from half filling the construction leads to a class of correlated singlet fluid states which are identified with generalized flux phases of the diluted resonating-valence-bond.

DOI
10.1103/physrevb.40.2670

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Physical review. B, Condensed matter•Nov 1, 1989•108 citations
We discuss a representation of the large-U Hubbard Hamiltonian for fermions on a two-dimensional lattice, in which the Gutzwiller constraint is imposed as a kinematical constraint on the motion of the underlying quasiparticles. At the half-filled band this construction identifies the ``Kalmeyer-Laughlin'' singlet as a unique Jastrow state satisfying the quantum constraints of the large-U problem. Away from half filling the construction leads to a class of correlated singlet fluid states which are identified with generalized flux phases of the diluted resonating-valence-bond.
We study the strongly correlated two-dimensional Hubbard model for general band filling by a transformation of the model to a spin-free representation. A pair transformation is constructed that maps a strong-coupling Hubbard problem in which the particles obey Fermi statistics onto a spin-free representation in which the charge degrees of freedom are spinless fermions, while constraining the physical system to an eigenstate of total spin. The Gutzwiller constraint is thus satisfied kinematically in the transformed problem for a class of Pauli-allowed many-fermion spatial wave functions. We find that the required pair transformation within the spin-singlet sector leads to correlated many-body states with broken time-reversal symmetry. For small band filling in the spin-singlet sector, the transformed problem for the charge degrees of freedom is formally identical to a problem for indistinguishable noninteracting 1/2 anyons (semions). For small deviations from half filling, the charge degrees of freedom (holes) in the singlet sector are again naturally represented as 1/2 anyons but in the presence of a strong uniform background U(1) gauge field. Exactly at half filling the charge degrees of freedom are quenched, and the formulation reduces to the spin-singlet wave function for the two-dimensional lattice first proposed by Kalmeyer and Laughlin. The one- and two-hole dynamics around this neutral chiral state on the two-dimensional lattice are considered in detail. Finally, numerical calculations are reported to test the accuracy of these states as approximations to the ground state of the Hubbard Hamiltonian. Over a range of band fillings we find that Gutzwiller projections of free-particle determinants provide improved hole kinetic energies, while a projection of the \ensuremath{\pi} flux phase provides improved spin-exchange energies for the pure Hubbard problem.
We present a formulation of the resonating-valence-bond theory of the large-UUU one-band Hubbard model in two dimensions, in which the correlated ground state of the system is represented as a fluid of mobile singlet bonds. We describe this fluid as a quantum fluid of interacting hardcore bosons, and a ground-state wave function for the interacting bosons is studied in which two-body correlations are introduced by applying techniques previously developed in Laughlin's theory of the fractional quantum Hall problem. The resulting many-particle state in this formulation exhibits an incipient momentum space condensation and a class of particlelike excitations in the form of quantized vortices which possess fractional particle number, and interesting dynamics. Application of this model to the doped state reveals a mechanism by which the electrostatic repulsive interactions between the charged quasiparticles in the doped fluid stabilize the resonating state relative to the doped N\'eel state at discrete well-correlated "commensurate" hole concentrations. A superconducting state in this doped fluid arises from a condensation which pairs the charged quasiparticles; it is identified as the most stable of a hierarchy of possible condensed quasiparticle states. The condensed state exhibits many properties associated with conventional superconductivity, including dissipationless flow of current, Meissner effect, and flux quantization in units of hc2e\frac{\mathrm{hc}}{2e}2ehc​.
Gutzwiller variational method is applied to an effective two-dimensional Hubbard model to examine the recently proposed gossamer superconductor by Laughlin (LANL cond-mat/0209269). The ground state at half filled electron density is a gossamer superconductor for smaller intrasite Coulomb repulsion U and a Mott insulator for larger U. The gossamer superconducting state is similar to the resonating valence bond superconducting state, except that the chemical potential is approximately pinned at the mid of the two Hubbard bands away from the half filled.
One dimensional chiral Hubbard model reduces to the Haldane-Shastry spin chain at half-filling with large but finite on-site energy UUU.In this talk, we show that the Gutzwiller-Jastrow wavefunctions are the eigen-states of the Hubbard model at U=+∞U=+\inftyU=+∞ at less than half-filling. The full energy spectrum and an infinite set of mutually commuting constants of motion are also given in this limit for the system.
Laughlin's construction of exact gossamer ground states is applied to normal metals. We show that for each variational parameter 0<=g<=1, the paramagnetic or ferromagnetic Gutzwiller wave function is the exact ground state of an extended Hubbard model with correlated hopping, with arbitrary particle density, non-interacting dispersion, and lattice dimensionality. The susceptibility and magnetization curves are obtained, showing that the Pauli susceptibility is enhanced by correlations. The elementary quasiparticle excitations are gapless, except for a half-filled band at g=0, where a Mott transition from metal to insulator occurs.