Understanding High-Temperature Superconductors with Quantum Cluster Theories

TL;DR

This paper reviews quantum cluster theories applied to the 2D Hubbard model, revealing phenomena like antiferromagnetism, superconductivity, and pseudogap behavior, and discusses insights into the pairing mechanism using advanced simulation and diagrammatic methods.

Contribution

It provides a systematic review of dynamical cluster simulations of the 2D Hubbard model, connecting these results to phenomena observed in cuprates and exploring the pairing mechanism.

Findings

Reproduction of cuprate-like phenomena such as pseudogap and superconductivity

Insights into the structure of the pairing mechanism from combined methods

Demonstration of the effectiveness of quantum cluster theories in correlated systems

Abstract

Quantum cluster theories are a set of approaches for the theory of correlated and disordered lattice systems, which treat correlations within the cluster explicitly, and correlations at longer length scales either perturbatively or within a mean-field approximation. These methods become exact when the cluster size diverges, and most recover the corresponding (dynamical) mean-field approximation when the cluster size becomes one. Here we will review systematic dynamical cluster simulations of the two-dimensional Hubbard model, that display phenomena remarkably similar to those found in the cuprates, including antiferromagnetism, superconductivity and pseudogap behavior. We will then discuss results for the structure of the pairing mechanism in this model, obtained from a combination of dynamical cluster results and diagrammatic techniques.