Publications by Michael Lubasch

Tensor network states in time-bin quantum optics

PHYSICAL REVIEW A 97 (2018) ARTN 062304

M Lubasch, AA Valido, JJ Renema, WS Kolthammer, D Jaksch, MS Kim, I Walmsley, R Garcia-Patron

Multigrid renormalization

Journal of Computational Physics 372 (2018) 587-602

M Lubasch, P Moinier, D Jaksch

© 2018 Elsevier Inc. We combine the multigrid (MG) method with state-of-the-art concepts from the variational formulation of the numerical renormalization group. The resulting MG renormalization (MGR) method is a natural generalization of the MG method for solving partial differential equations. When the solution on a grid of N points is sought, our MGR method has a computational cost scaling as O(log⁡(N)), as opposed to O(N) for the best standard MG method. Therefore MGR can exponentially speed up standard MG computations. To illustrate our method, we develop a novel algorithm for the ground state computation of the nonlinear Schrödinger equation. Our algorithm acts variationally on tensor products and updates the tensors one after another by solving a local nonlinear optimization problem. We compare several different methods for the nonlinear tensor update and find that the Newton method is the most efficient as well as precise. The combination of MGR with our nonlinear ground state algorithm produces accurate results for the nonlinear Schrödinger equation on N=1018grid points in three spatial dimensions.

Diagonalization of complex symmetric matrices: Generalized Householder reflections, iterative deflation and implicit shifts


JH Noble, M Lubasch, J Stevens, UD Jentschura

Systematic construction of density functionals based on matrix product state computations


M Lubasch, JI Fuks, H Appel, A Rubio, JI Cirac, M-C Banuls