# Crossover Induced Electron Pairing and Superconductivity by Kinetic Renormalization in Correlated Electron Systems

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## Abstract

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## 1. Introduction

## 2. Model Hamiltonians

## 3. Optimization Variational Monte Carlo Method

## 4. Antiferromagnetic Crossover

## 5. Correlated Superconductivity

## 6. Phase Separation

## 7. Summary

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

VMC | variational Monte Carlo method |

AF | antiferromagnetic |

SC | superconductivity or superconducting |

2D | two-dimensional |

AFI | antiferromagnetic insulator |

PI | paramagnetic insulator |

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**Figure 1.**AF and SC order parameters as a function of $U/t$ on a $10\times 10$ lattice with the periodic boundary condition in one direction and antiperiodic one in the other direction [38]. In Reference [38] $\Delta $ was shown as a function of U in the range $0<U<20$. We modified the figure to include the range $20<U<25$. ${\Delta}_{AF}$ has a peak when U is of the order of the bandwidth $U/t\sim 10$. AF(G) in the figure shows the result obtainee for the simple Gutzwiller function.

**Figure 2.**Antiferromagnetic order parameters as a function of the hole density $1-{n}_{e}$ on a $10\times 10$ lattice for ${t}^{\prime}=0$. We put $U/t=12,14$ and 18.

**Figure 3.**Antiferromagnetic order parameters as a function of the hole density $1-{n}_{e}$ on a $10\times 10$ lattice for ${t}^{\prime}=-0.2t$. We put $U/t=12,14$ and 18.

**Figure 4.**Antiferromagnetic and paramagnetic insulator states in the plane of ${t}_{pp}$ and $|{t}_{d}^{\prime}|$ for the d-p model. We put ${U}_{d}=8$, ${U}_{p}=0$, ${\u03f5}_{p}-{\u03f5}_{d}=1$ and ${t}_{d}^{\prime}<0$ on a $6\times 6$ lattice with 108 atoms in total. The energy unit is given by ${t}_{dp}$.

**Figure 5.**The condensation energy per site as a function of the hole density $x=1-{n}_{e}$ on a $10\times 10$ lattice for the 2D Hubbard model. The SC and AF condensation energies are shown. We set ${t}^{\prime}=0$ and $U/t=18$.

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**MDPI and ACS Style**

Yanagisawa, T.; Miyazaki, M.; Yamaji, K.
Crossover Induced Electron Pairing and Superconductivity by Kinetic Renormalization in Correlated Electron Systems. *Condens. Matter* **2018**, *3*, 26.
https://doi.org/10.3390/condmat3030026

**AMA Style**

Yanagisawa T, Miyazaki M, Yamaji K.
Crossover Induced Electron Pairing and Superconductivity by Kinetic Renormalization in Correlated Electron Systems. *Condensed Matter*. 2018; 3(3):26.
https://doi.org/10.3390/condmat3030026

**Chicago/Turabian Style**

Yanagisawa, Takashi, Mitake Miyazaki, and Kunihiko Yamaji.
2018. "Crossover Induced Electron Pairing and Superconductivity by Kinetic Renormalization in Correlated Electron Systems" *Condensed Matter* 3, no. 3: 26.
https://doi.org/10.3390/condmat3030026