Foundations and Applications of Quantum Science

Simulation of strongly correlated quantum systems              

Frank Verstraete

The proposed project targets the development of novel methods for simulating strongly correlated quantum many-body systems. The central topic will be devising techniques for simulating properties of lattice and continuum systems in 1 and 2 dimensions, with a focus on the description of low-energy excitations and low-energy non-equilibrium behavior. The state-of-the-art method for simulating ground states of quantum spin systems is the matrix product state (MPS) formalism, which has proven to be able to model quantum simulation experiments with optical lattices and ion traps. The focus of this proposal will be to extend the scope of those MPS methods to extract information about the dispersion relations and Green’s functions.This will be pursued in the first part of this proposal. In the second part, we will study continuum versions of the MPS formalism, which is leading to a non-commutative version of the famous Gross-Pitaevskii (GP) equation and, for excitations, to nontrivial generalizations of the Bogoliubov-deGennes (BdG) equations. A third part of the proposal is concerned with the theoretical understanding of elementary excitations and quasiparticles in strongly correlated quantum many-body systems from the point of view of the theory of entanglement.

Supporting Organizations







Created by: Rainer Blatt
Last modified 2013-01-31T14:17:54 by Tracy Northup