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Physical review. B, Condensed matter

Singlet wave function of the infinite-UHubbard model in two dimensions

弘之 森

Published Nov 1, 1992• 1 citation
Publisher

Abstract

Introducing an auxiliary field to describe strongly correlated electrons, we investigate variational states of the infinite-U Hubbard model in two dimensions. A mean-field analysis shows that the energetically favored electron-decomposition schemes are the slave-boson method and a slave-semion method, in the latter of which an electron is treated as a composite of two kinds of semions. Along each scheme we derive variational singlet wave functions. Variational Monte Carlo calculation shows that the projected Fermi sea is the lowest-energy state among the obtained variational wave functions.

DOI
10.1103/physrevb.46.10952

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Introducing an auxiliary field to describe strongly correlated electrons, we investigate variational states of the infinite-U Hubbard model in two dimensions. A mean-field analysis shows that the energetically favored electron-decomposition schemes are the slave-boson method and a slave-semion method, in the latter of which an electron is treated as a composite of two kinds of semions. Along each scheme we derive variational singlet wave functions. Variational Monte Carlo calculation shows that the projected Fermi sea is the lowest-energy state among the obtained variational wave functions.
We introduce Gutzwiller-correlated wave functions for the variational investigation of general multi-band Hubbard models. We set up a diagrammatic formalism which allows us to evaluate analytically ground-state properties in the limit of infinite spatial dimensions. In this limit recent results obtained within the Gutzwiller approximation are seen to become exact for these wave functions. We further show that the slave-boson mean-field theory for degenerate bands becomes variationally controlled at zero temperature in infinite dimensions. Lastly, we briefly comment on the variational approach to the Anderson transition in strongly correlated electron systems.
A variational Monte-Carlo method is formulated to study superconductivity in strongly correlated electrons. An application is made to the strongly correlated Hubbard model on two-dimensional square lattice, by employing the simplest mean-field-type trial wave function, i.e. the Gutzwiller-projected BCS wave function. Among the various choices examined, the d-wave-type superconductivity turns out to be the most favorable. The nature of the superconducting order parameter and spin correlations is also examined.
We study a class of variational wave functions for strongly correlated systems by expanding the electron operators as composites of spin-1/2 Fermi fields and spinless Fermi fields. The composite particles automatically satisfy the local constraint of no double occupancy and include correlations between opposite-spin particles in a very physical way. We calculate the energy and correlation functions for the one-dimensional U=\ensuremath{\infty} Hubbard model, where a comparison with exact results is made. The method is computationally very tractable and can readily be generalized to higher dimensions.
We investigate Gutzwiller-correlated wave functions as variational ground states for the periodic Anderson model. We extend a recently developed technique for the Hubbard model to the case of two hybridized bands with degeneracy N. We calculate expectation values in the following limits: dilute system (single-impurity case), large degeneracy N, and large dimension d. The mean-field results using the slave-boson approach of Coleman and of Kotliar and Ruckenstein are reproduced in the large-N and large-d limit, respectively. These techniques, therefore, obey variational principles at T=0 in the respective limits and their applicability for T>0 is naturally limited to the Fermi-liquid regime. Evaluations of Gutzwiller-correlated wave functions using the ``Gutzwiller approximation'' are seen to become exact in the limit of large dimensions. A systematic expansion in 1/d can be performed for N=2. In general, corrections are small, of order 1/(dN).
The effect of electron correlations in the infinite-dimension (d=∞) Hubbard model at finite temperatures has been investigated with the use of a theory which was recently proposed by the present author generalizing the slave-boson functional-integral method. Sublattice magnetizations, double occupancies and band-narrowing factors are computed as functions of the interaction, U, and the temperature, T. Calculated results are exact in the limits of U→0 and U→∞, and in the limits of T=0 and T→∞ they are expected to be very accurate owing to the nature of our mean-field-type theory for infinite-dimension systems. Similarities and differences between the calculated results for d=3 and d=∞ are also discussed.
The ground state of the Hubbard model on one-dimensional and two-dimensional square lattices is studied with the effective Hamiltonian derived for the strong correlation regime and Gutzwiller-type wave function. The non-half-filled band as well as the half-filled band is discussed. The variational Monte-Carlo method enables us to evaluate the energy for the singlet liquid (resonating-valence-bond state) and for Néel state. The result shows that the stability of the singlet liquid depends on the dimensionality of the system.