Low Energy Excitation Spectra from Tangent Plane Methods, Part I

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 I: After explaining our method, I will compare it with other tangent plane approaches and discuss key advantages in the context of the paradigmatic Bose-Hubbard model.