Variational Monte Carlo Study on the Superconductivity in the Two-Dimensional Hubbard Model

TL;DR

This study uses variational Monte Carlo methods to explore superconductivity in the 2D Hubbard model, identifying optimal parameters and the competition with magnetic states, with results aligning with experimental superconductors.

Contribution

It provides new insights into the parameter dependence of superconductivity in the 2D Hubbard model using variational Monte Carlo, highlighting the role of next nearest neighbor transfer t' and electron density.

Findings

Maximum energy gain at U=8 and t'~-0.10

Superconductivity extends from rho~0.76 to 0.87 for certain t' values

Results align with condensation energies in YBa2Cu3O7

Abstract

The possibility of superconductivity (SC) in the 2D Hubbard model (2DH) was investigated by means of the variational Monte Carlo method. The energy gain of the d-wave SC state, obtained as the difference of the minimum energy with a finite gap and that with zero gap, was examined with respect to dependences on U, electron density rho and next nearest neighbor transfer t' mainly on the 10 x 10 lattice. It was found to be maximized around U = 8 (in energy unit of t). It sharply increased for negative values of t' and had a broad peak for t' ~ -0.10. For these values of t' the energy gain was a smooth increasing function of rho almost independent of the shell structure in the region starting from ~ 0.76 up to 0.92. This clearly indicates that the result is already close to the value in the bulk limit. For t' = 0, the energy gain depended on the electronic shell state. Competition between the SC and the SDW states was also investigated. When t' = 0, the ground state is SDW in the range of rho \geq ~ 0.84$. The SC region slightly extends up to ~ 0.87 for t' ~ -0.10. Consequently the present results strongly indicate that the 2DH with t' ~ -0.1 drives SC by itself in the rho region from ~ 0.76 to ~ 0.87. The energy gain in the SC state with suitable parameters is found to be in reasonable agreement with the condensation energy in the SC state of YBa2Cu3O7. The corresponding t-J model proves to give an order-of-magnitude larger energy gain, which questions its validity.