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author:
- 'Kunihiko [Yamaji]{}$^{a,b}$[^1], Takashi [Yanagisawa]{}$^{a}$, Takeshi [Nakanishi]{}$^{a}$[^2] and Soh [Koike]{}$^{b,a}$'
title: ' Variational Monte Carlo Study on the Superconductivity in the Two-Dimensional Hubbard Model '
---

Introduction
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Recently the mechanisms of superconductivity (SC) in high-temperature cuprate superconductors and organic superconductors have been extensively studied using various two-dimensional (2D) models of electronic interactions. The 2D Hubbard model is the simplest and the most fundamental one among such models. Early studies of this model using the quantum Monte Carlo (M.C.) method indicated the existence of an attractive interaction for SC \[\]. However, this possibility has been controversial. Some authors asserted from quantum M.C. results that the enhanced SC correlation does not develop into the predominant one at low temperatures or in the ground state of this model \[\]. Some authors supported this possibility by numerical results using the variational Monte Carlo (M.C.) method \[\]. Since it is of prime importance to establish the simplest electronic model for superconductivity and since these early studies had shortcomings due to the restrictions to the investigated parameter space, the problem deserves more extensive investigation from various aspects such as dependences on the system size, the on-site Coulomb energy $U$, the electron density $\rho$ 