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The Review of High Pressure Science and Technology

Off-Diagonal Wave Functions and Superconductivity in the Variational Monte Carlo Calculations.

Takashi Yanagisawa, Takeshi Nakanishi, Soh Koike, Yamaji K.

Published Jan 1, 1998• 5 citations
Publisher

Abstract

We investigate the two-dimensional Hubbard model by the variational Monte Carlo method. We consider off-diagonal wave functions where we improve the Gutzwiller wave function by multiplying off-diagonal factors. In the 4×4 system, we compare our results with the exact diagonalization. The variational energies are fairly close to the exact values. We show the results for the 10×10 Hubbard model.

DOI
10.4131/jshpreview.7.154

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We investigate the ground-state phase diagram of the two-dimensional Hubbard model based on the optimization variational Monte Carlo method. We use a wave function that is an off-diagonal type given as ψ=exp⁡(−λK)PGψ0ψ=\exp(-λK)P_Gψ_0ψ=exp(−λK)PG​ψ0​, where ψ0ψ_0ψ0​ is a one-particle state, PGP_GPG​ is the Gutzwiller operator, KKK is the kinetic operator, and λλλ is a variational parameter. The many-body effect plays an important role as an origin of spin correlation and superconductivity in correlated electron systems. We examine the competition between the antiferromagnetic state and superconducting state by varying the Coulomb repulsion UUU, the band parameter t′t't′ and the electron density nen_ene​. We show a phase diagram that includes superconducting and antiferromagnetic phases and that t′=0t'=0t′=0 is most favorable for superconductivity.
A d -wave state wave function with multiplicative correlation factors for the Hubbard model is investigated using a variational Monte Carlo method. Employing a simple Gutzwiller-BCS wave function as a starting wave function, we consider improved wave functions with off-diagonal correlation factors. The Monte Carlo simulations are carried out on a square lattice with size 10×10 for U =8 and next nearest neighbor transfer t '=-0.09. The ground-state energy is evaluated from an extrapolation. Our wave functions show that pair correlation functions are enhanced for a negative value of t '.
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