Low Energy Excitation Spectra from Tangent Plane Methods, Part II*

Variational methods are extensively used in quantum many body problems to overcome the exponential growth of the Hilbert space with the system size. By focusing on a suitable sub-manifold of states, we can study properties of ground states and low excited states. Here, we will introduce a novel framework to approximate the low lying energy spectrum by studying the linearized Hamiltonian flow on the tangent plane to this manifold at the ground state.
Part II: I will focus on the underlying geometry and explain how the approximate ground state and the low energy spectra arise from invariant geometric structures of the variational manifold.