Double Feature: Geometry of variational manifolds and the Bose-Hubbard model (Dr. Lucas Hackl)
Dr. Lucas Hackl
Theory Division, MPQ
Max Planck Institute of Quantum Optics
Herbert Walther Lecture Hall
A key challenge in the theoretical study of quantum many body systems is to overcome the exponential growth of the Hilbert space with the system size. Many successful approaches are variational, i.e., they are based on choosing suitable families of states that capture key properties of the system. Prominent examples range from Gaussian states to matrix product states and tensor networks.
In this talk, I will review the geometric structures of variational
manifolds and how we can use them to systematically (a) estimate ground state
energies, (b) compute approximate excitation spectra, (c) predict the linear
response of these systems and (d) study quenches in the presence of conserved
quantities. Taking the Bose-Hubbard model as example, I show how our methods
give rise to a systematic extension of the traditional Bogoliubov theory.
[based on work with Tommaso Guaita, Tao Shi, Claudius Hubig, Eugene Demler and