# Geometry of variational methods

- Date: May 24, 2019
- Time: 11:00 - 11:25
- Speaker: Dr. Lucas Hackl
- MPHQ Postdoctoral Fellow

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 and (c) predict the linear response of
these systems. Taking the Bose-Hubbard model as example, I show how this
gives rise to a systematic extension of the traditional Bogoliubov
theory.[based on work with Tommaso Guaita, Tao Shi, Claudius Hubig,
Eugene Demler and Ignacio Cirac]