Correlated-Electron Systems and High Temperature Superconductivity

TL;DR

This paper reviews recent theoretical advances in understanding high-temperature superconductivity in correlated-electron systems, focusing on numerical methods applied to models like the Hubbard and d-p models, revealing insights into phase diagrams and pairing mechanisms.

Contribution

It introduces new numerical approaches and detailed phase diagrams for correlated-electron models, advancing understanding of high-temperature superconductivity mechanisms.

Findings

Superconducting condensation energy aligns with experimental estimates for YBa2Cu3O7.

Stripe and checkerboard states are stable in the under-doped region.

Pair correlation function increases with hole doping, not at half-filling.

Abstract

We present recent theoretical results on superconductivity in correlated-electron systems, especially in the two-dimensional Hubbard model and the three-band d-p model. The mechanism of superconductivity in high-temperature superconductors has been extensively studied on the basis of various electronic models and also electron-phonon models. In this study we investigate the properties of superconductivity in correlated-electron systems by using numerical methods such as the variational Monte Carlo method and the quantum Monte Carlo method. The Hubbard model is one of basic models for strongly correlated electron systems, and is regarded as the model of cuprate high temperature superconductors. The d-p model is more realistic model for cuprates. The superconducting condensation energy obtained by adopting the Gutzwiller ansatz is in reasonable agreement with the condensation energy estimated for YBa_2Cu_3O_7. We show the phase diagram of the ground state using this method. We have further investigated the stability of striped and checkerboard states in the under-doped region. The relationship of the hole density x and incommensurability \delta, \delta\sim x, is satisfied in the lower doping region, as indicated by the variational Monte Carlo calculations. We have performed a variational Monte Carlo simulation on a two-dimensional t-t'-t"-U Hubbard model with a Bi-2212 type band structure and found that the 4\times 4 period checkerboard spin modulation, that is characterized by multi Q vectors, is stabilized. We also present a new algorithm of the diagonalization quantum Monte Carlo method that is a method for the evaluation of expectation values without the negative sign difficulty. We show that the pair correlation function is not enhanced at half-filling, and is indeed enhanced with hole doping.