Low-rank eigenvalue solvers for block-sparse matrix product states
Provides a theoretical analysis and practical algorithm for solving Schrödinger equations with matrix product states, relevant to quantum chemistry and condensed matter physics.
The paper develops low-rank eigenvalue solvers for block-sparse matrix product states, achieving accurate eigenfunction approximations with adapted ranks. Numerical tests demonstrate effectiveness on fermionic Schrödinger equations.
We consider an iterative eigensolver for Schrödinger equations that constructs low-rank approximations of eigenfunctions with accuracy-adapted ranks, with particular focus on fermionic Schrödinger equations in second-quantized form and on matrix product state approximations enforcing particle number conservation. We provide a complete analysis of a solver based on preconditioned inverse iteration combined with rank truncation and propose a generalization to subspace iteration for the joint approximation of several eigenspaces. The practical performance of the method is illustrated by numerical tests for several model problems.