A Wilsonian Approach to Crystal Structure Transformations driven by Strong Electron Correlations

Mathematical descriptions of the interplay between strong electron correlations and lattice degrees of freedom are of enormous importance in the development of new devices based on metal oxides such as VO$_{2}$ and the Cuprate superconductors. In this work the physics of tight-binding type electron momentum states interacting with lattice fluctuations is reformulated into an approach based on lattice QCD. Strong electron correlations act as a source for phonons, which are incorporated by using SU(2) bosons acting on neighbouring atomic sites. This allows the system to be described by a Hamiltonian which describes strong interactions between SU(2) Yang-Mills bosons near T$_{c}$ resulting from electron correlations. Monte Carlo and GW calculations show that at low Temperature the electron-electron interactions drive the system into a phase coherent phonon state, breaking the lattice symmetry, and a band gap opens. This formalism is intrinsically able to combine strong-electron correlations with lattice fluctuations in a manner which describes symmetry-breaking structural phase transitions which manifest spin- and charge ordering.