Investigation of Strongly Correlated Electron Systems with Cellular Dynamical Mean Field Theory

TL;DR

This thesis develops and applies Cellular Dynamical Mean Field Theory (CDMFT) to study strongly correlated electron systems, revealing insights into the Mott transition and unconventional superconductivity in cuprates.

Contribution

It introduces CDMFT with exact diagonalization, extending DMFT to include short-range spatial correlations in the Hubbard model.

Findings

CDMFT accurately captures short-range correlations in the Hubbard model.

The doped Mott insulator exhibits anomalous properties near the transition.

A d-wave superconducting state is supported within CDMFT, differing from BCS theory.

Abstract

In this thesis we study the strongly-correlated-electron physics of the longstanding H-Tc-superconductivity problem using a non-perturbative method, the Dynamical Mean Field Theory (DMFT), capable to go beyond standard perturbation-theory techniques. DMFT is by construction a local theory which neglects spatial correlation. Experiments have however shown that the latter is a fundamental property of cuprate materials. In a first step, we approach the problem of spatial correlation in the normal state of cuprate materials using a phenomenological Fermi-Liquid-Boltzmann model. We then introduce and develop in detail an extension to DMFT, the Cellular Dynamical Mean Field Theory (CDMFT), capable of considering short-ranged spatial correlation in a system, and we implement it using the exact diagonalization algorithm . After benchmarking CDMFT with the exact one-dimensional solution of the Hubbard Model, we employ it to study the density-driven Mott metal-insulator transition in the two-dimensional Hubbard Model, focusing in particular on the anomalous properties of the doped normal state close to the Mott insulator. We finally study the superconducting state. We show that within CDMFT the one-band Hubbard Model supports a d-wave superconductive state, which strongly departs from the standard BCS theory. We conjecture a link between the instabilities found in the normal state and the onset of superconductivity.