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Australian Journal of Physics

Variational Solutions of the Hubbard Model for the bcc Lattice

C. M. Villet, W.‐H. Steeb

Published Jun 1, 1990• 0 citations
Publisher

Abstract

A variational method is used to find approximative solutions of the Hubbard model for the ground state of the bcc lattice in the weak and strong coupling limits. The neutral case (a half-filled band) is found to be antiferromagnetic for all values of the coupling constant. However, for other choices of the band· filling second phase transitions between different magnetic structures are found if the coupling constant is varied.

DOI
10.1071/ph900333

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A variational method is used to find approximative solutions of the Hubbard model for the ground state of the bcc lattice in the weak and strong coupling limits. The neutral case (a half-filled band) is found to be antiferromagnetic for all values of the coupling constant. However, for other choices of the band· filling second phase transitions between different magnetic structures are found if the coupling constant is varied.
We investigate the phase diagram of the square lattice bilayer Hubbard model at half-filling with the variational Monte Carlo method for both the magnetic and the paramagnetic case as a function of the interlayer hopping and on-site Coulomb repulsion U . With this study we resolve some discrepancies in previous calculations based on the dynamical mean-field theory, and we are able to determine the nature of the phase transitions between metal, Mott insulator and band insulator. In the magnetic case we find only two phases: an antiferromagnetic Mott insulator at small for any value of U and a band insulator at large . At large U values we approach the Heisenberg limit. The paramagnetic phase diagram shows at small a metal to Mott insulator transition at moderate U values and a Mott to band insulator transition at larger U values. We also observe a re-entrant Mott insulator to metal transition and metal to band insulator transition for increasing in the range of . Finally, we discuss the phase diagrams obtained in relation to findings from previous studies based on different many-body approaches.
We supplement (and critically overview) the existing extensive analysis of antiferromagnetic solution for the Hubbard model with a detailed discussion of two specific features, namely (i) the evolution of the magnetic (Slater) gap (here renormalized by the electronic correlations) into the Mott-Hubbard or atomic gap, and (ii) a rather weak renormalization of the effective mass by the correlations in the half-filled-band case, which contrasts with that for the paramagnetic case. The mass remains strongly enhanced in the non-half-filled-band case. We also stress the difference between magnetic and non-magnetic contributions to the gap. These results are discussed within the slave boson approach in the saddle-point approximation, in which there appears a non-linear staggered molecular field due to the electronic correlations that leads to the appearance of the magnetic gap. They reproduce correctly the ground-state energy in the limit of strong correlations. A brief comparison with the solution in the limit of infinite dimensions and the corresponding situation in the doubly-degenerate-band case with one electron per atom is also made. 1 1
We study the ground-state properties of the Hubbard model on the honeycomb lattice at half filling. Using the variational cluster approximation, We study the semimetal-insulator transition and antiferromagnetism as functions of the on-site Coulomb interaction U . When U is switched on, a small, but finite, single-particle gap appears; thus, we conclude that a tiny gap appears with arbitrary small U > 0. With further increases in U , the system goes into the antiferromagnetic state. We find that the staggered magnetization increases continuously with increasing U and that the antiferromagnetic phase transition is of the second order.
Abstract. We investigate the phase diagram of the square lattice bilayer Hubbard model at half filling with the variational Monte Carlo method for both the magnetic and the paramagnetic case as a function of the interlayer hopping t ⊥ and on-site Coulomb repulsion U. With this study we resolve some discrepancies in previous calculations based on the dynamical mean field theory, and we are able to determine the nature of the phase transitions between metal, Mott insulator and band insulator. In the magnetic case we find only two phases: An antiferromagnetic Mott insulator at small t ⊥ for any value of U and a band insulator at large t⊥. At large U values we approach the Heisenberg limit. The paramagnetic phase diagram shows at small t ⊥ a metal to Mott insulator transition at moderate U values and a Mott to band insulator transition at larger U values. We also observe a re-entrant Mott insulator to metal transition and metal to band insulator transition for increasing t ⊥ in the range of 5.5t < U < 7.5t. Finally, we discuss the obtained phase diagrams in relation to previous studies based on different many-body approaches. PACS numbers: 71.10.Fd, 71.27.+a, 71.30.+h 1.
A variational ground state of the repulsive Hubbard model on a square lattice is investigated numerically for an intermediate coupling strength (U=8t)(U=8t)(U=8t) and for moderate sizes (from $6\ifmmode\times\else\texttimes\fi{}6$ to $10\ifmmode\times\else\texttimes\fi{}10$). Our ansatz is superior to other widely used variational wave functions. The results for order parameters and correlation functions provide insight into the antiferromagnetic state at half-filling as well as strong evidence for a superconducting phase away from half-filling.