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Physical review. B, Condensed matter

Variational wave functions for the Mott transition: The 1/rHubbard chain

Michael Dzierzawa, D. Baeriswyl, Michela Di Stasio

Published Jan 15, 1995• 21 citations
Publisher

Abstract

The exactly soluble 1/r Hubbard chain is studied at half filling. Two classes of variational wave functions are introduced, one representing the metallic phase, the other the insulating phase. An iterative scheme is found to converge rapidly towards the exact results both for the ground-state energy and the double occupancy. The insulating and metallic phases are connected by a duality relation, which allows one to locate exactly the critical value of the Hubbard parameter U.

DOI
10.1103/physrevb.51.1993

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The exactly soluble 1/r Hubbard chain is studied at half filling. Two classes of variational wave functions are introduced, one representing the metallic phase, the other the insulating phase. An iterative scheme is found to converge rapidly towards the exact results both for the ground-state energy and the double occupancy. The insulating and metallic phases are connected by a duality relation, which allows one to locate exactly the critical value of the Hubbard parameter U.
An approximate solution scheme, similar to the Gutzwiller approximation, is presented for the Baeriswyl and the Baeriswyl-Gutzwiller variational wave functions. The phase diagram of the one-dimensional Hubbard model as a function of interaction strength and particle density is determined. For the Baeriswyl wave function a metal-insulator transition is found at half filling, where the metallic phase (U<Uc)(U<{U}_{c})(U<Uc​) corresponds to the Hartree-Fock solution, the insulating phase is one with finite double occupations arising from bound excitons. This transition can be viewed as the ``inverse'' of the Brinkman-Rice transition. Close to but away from half filling, the U>UcU>{U}_{c}U>Uc​ phase displays a finite Fermi step, as well as double occupations originating from bound excitons. As the filling is changed away from half-filling bound excitons are suppressed. For the Baeriswyl-Gutzwiller wave function at half filling a metal-insulator transition between the correlated metallic and excitonic insulating state is found. Away from half-filling bound excitons are suppressed quicker than for the Baeriswyl wave function.
We study ground-state properties of the two-dimensional Hubbard model at half filling by improving variational Monte Carlo method and by implementing quantum-number projection and multi-variable optimization. The improved variational wave function enables a highly accurate description of the Mott transition and strong fluctuations in metals. We clarify how anomalous metals appear near the first-order Mott transition. The double occupancy stays nearly constant as a function of the on-site Coulomb interaction in the metallic phase near the Mott transition in agreement with the previous unbiased results. This unconventional metal at half filling is stabilized by a formation of ``electron-like pockets'' coexisting with an arc structure, which leads to a prominent differentiation of electrons in momentum space. An abrupt collapse of the ``pocket'' and ``arc'' drives the first-order Mott transition.
Two very different methods — exact diagonalization on finite chains and a variational method — are used to study the possibility of a metal-insulator transition in the symmetric half-filled periodic Anderson-Hubbard model. With this aim we calculate the density of doubly occupied d sites (gn d ) as a function of various parameters. In the absence of on-site Coulomb interaction (U f ) between f electrons, the two methods yield similar results. The double occupancy of d levels remains always finite just as in the one-dimensional Hubbard model. Exact diagonalization on finite chains gives the same result for finite U f , while the Gutzwiller method leads to a Brinkman-Rice transition at a critical value (U ), which depends on U f and V.
Two very different methods – exact diagonalization on finite chains and a variational method – are used to study the possibility of a metal-insulator transition in the symmetric half-filled periodic Anderson-Hubbard model. With this aim we calculate the density of doubly occupied d sites (νd) as a function of various parameters. In the absence of on-site Coulomb interaction (Uf ) between f electrons, the two methods yield similar results. The double occupancy of d levels remains always finite just as in the one-dimensional Hubbard model. Exact diagonalization on finite chains gives the same result for finite Uf , while the Gutzwiller method leads to a Brinkman-Rice transition at a critical value (U c d ), which depends on Uf and V .
We investigate the Mott transition in a two-dimensional two-orbital Hubbard model on a square lattice at half filling by using the variational Monte Carlo method. As a variational trial wave function, we consider Gutzwiller's on-site correlations and nearest-neighbor doublon-holon correlations. We calculate the ground-state energy and the other physical quantities, all of which clearly signal a first-order Mott transition. We thus obtain the phase diagram at zero temperature, where we find the coexistence region of the metal and the Mott insulator. We discuss how Hund's coupling affects the nature of the Mott transition in this system.
We study the one-band Hubbard model at half filling with hopping asymmetry and its effective model at finite but large UUU up to the second order of tmix∕U{t}_{\text{mix}}∕Utmix​∕U. Two variational wave functions, the resonating valence bond (RVB) wave function and antiferromagnetic (AF) RVB coexisted wave function, are studied by variational Monte Carlo method on $L\ifmmode\times\else\texttimes\fi{}L$ square lattices up to L=12L=12L=12. Based on these two wave functions, the phase diagrams for both models are presented. For the Hubbard model, we find that there is a metal-insulator transition when the hopping parameter tmix{t}_{\text{mix}}tmix​ which changes the local double occupant vanishes while only a metal-insulator crossover is explored for any finite tmix{t}_{\text{mix}}tmix​. For the effective model in which the perturbation expansion is up to the second order of tmix∕U{t}_{\text{mix}}∕Utmix​∕U, a clear metal-insulator transition can be identified for both variational wave functions and the phase diagram can be drawn accordingly. In both models, we find that the systems are dominated by AF-RVB wave function when UUU is large while the RVB wave function is favored when UUU is small.