High Energy Theory Group Seminar: Expansion in large coordination number for quantum lattice systems

Abstract:

Quantum lattice systems are encountered in many field of physics: solid states, ultracold gases, 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 through a 1/Z expansion where Z is the coordination number i.e. number of interaction of a site with its neighbors. We apply this quite general method specifically to Bose and Fermi-Hubbard gases or Heisenberg spin magnets. In some cases, an analytical solution is found and allows to determine the quasi-excitation spectra and the quantum correlations. In the more general situation, a numerical solution yields the time-dependence of the correlations and provides an alternative to other techniques such as the density matrix renormalization group (or matrix-product state) method, especially for higher dimensions. 

We illustrate the powerfulness of these general concepts for a typical example of  prethermalisation after a quench.

Seminar Organizer: Shira Chapman