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.