Patrick Navez, Department of Physics, University of Crete
Expansion in large coordination number for quantum lattice system.
Quantum lattice systems are encountered in many fields of physics: solid states, ultracold gases, quantum optics, metamaterials and even quantum chromodynamics. For this class of systems, we establish a set of hierarchy equations describing the non equilibrium time evolution of the n-site spatial correlation reduced density matrices and solve it iteratively through a 1/Z expansion where Z is the coordination number (number of coupling of a site with the others). We illustrate the powerfulness of this method by focusing on the particular study of quench dynamics of the quantum Ising model and emphasize its usefulness to determine the entanglement property of an adiabatic quantum computer. We also show the potentiality of this method to solve the Bose and Fermi-Hubbard models where the latest is likely to describe the high Tc superconductivity.