Projector formalism for kept and discarded spaces of matrix product states

Gleis, Andreas; Li, Jheng-Wei und Delft, Jan von (2022): Projector formalism for kept and discarded spaces of matrix product states. In: Physical Review B, Bd. 106, Nr. 19, 195138

Abstract

Any matrix product state §psi > has a set of associated kept and discarded spaces, needed for the description of §psi >, and changes thereof, respectively. These induce a partition of the full Hilbert space of the system into mutually orthogonal spaces of irreducible n-site variations of §psi >. Here, we introduce a convenient projector formalism and diagrammatic notation to characterize these n-site spaces explicitly. This greatly facilitates the formulation ofMPS algorithms that explicitly or implicitly employ discarded spaces. As an illustration, we derive an explicit expression for the n-site energy variance and evaluate it numerically for a model with long-range hopping. We also describe an efficient algorithm for computing low-lying n-site excitations above a finite MPS ground state.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Physik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 530 Physik
• ISSN: 2469-9950
• Sprache: Englisch