Understanding High-Temperature Superconductors with Quantum Cluster Theories

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.

8 pages, 12 figures; submitted to proceedings of M2S-HTSC VIII, Dresden 2006

References in corpus (16)

• Correlated Electrons in High Temperature Superconductors
• Quantum Cluster Theories
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• Cluster Perturbation Theory for Hubbard models
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• The Structure of the Pairing Interaction in the 2D Hubbard Model
• A note on cluster methods for strongly correlated electron systems
• Phase Diagram of the Hubbard Model: Beyond the Dynamical Mean Field
• Fluctuation Exchange Analysis of Superconductivity in the Standard Three-Band CuO2 Model

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• Superconductivity in a Hubbard-Froehlich Model and in cuprates
• Multistage Electronic Nematic Transitions in Cuprate Superconductors: Functional-Renormalization-Group Analysis
• Competing Unconventional Charge-Density-Wave States in Cuprate Superconductors: Spin-Fluctuation-Driven Mechanism
• Odd-parity spin-loop-current order mediated by transverse spin fluctuations in cuprates and related electron systems
• $d$- and $p$-wave quantum liquid crystal orders in cuprate superconductors, $\kappa$-(BEDT-TTF)${}_2$X, and coupled chain Hubbard models: functional-renormalization-group analysis
• Development of spin fluctuations under the presence of $d$-wave bond order in cuprate superconductors