# Antiferromagnetism, Superconductivity and Phase Diagram in the Two-Dimensional Hubbard Model -- Off-Diagonal Wave Function Monte Carlo Studies of Hubbard Model III --

## TL;DR

This study uses an advanced variational Monte Carlo method to explore the phase diagram of the 2D Hubbard model, revealing the conditions favoring antiferromagnetism and superconductivity, with off-diagonal wave functions playing a key role.

## Contribution

It introduces an off-diagonal wave function approach in variational Monte Carlo to analyze competing phases in the Hubbard model, highlighting the importance of many-body effects.

## Key findings

- Superconductivity is most favored at zero next-nearest neighbor hopping ($t'=0$).
- The phase diagram includes both antiferromagnetic and superconducting phases.
- Many-body effects significantly influence spin correlations and superconductivity.

## Abstract

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 $\psi=\exp(-\lambda K)P_G\psi_0$, where $\psi_0$ is a one-particle state, $P_G$ is the Gutzwiller operator, $K$ is the kinetic operator, and $\lambda$ 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 $U$, the band parameter $t'$ and the electron density $n_e$. We show a phase diagram that includes superconducting and antiferromagnetic phases and that $t'=0$ is most favorable for superconductivity.