Project Details
Projekt
Refinement and extension of QC-DMRG based on recent quantum information concepts
Applicant
Dr. Christian Schilling
Subject Area
Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
Term
since 2019
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 414324924
It is the main goal of my proposed research programme to explain the surprising success of DMRG in quantum chemistry (QC-DMRG) with the ultimate aim of overcoming its main limitations. As I plan to show in a concise way, it is the strong conflict between energy minimization and fermionic exchange symmetry in systems of confined fermions which enforces a reduction of particle and orbital/mode entanglement. Hence, similar to proper lattice systems, a local structure emerges in QC-DMRG on the underlying artificial one-dimensional lattice built from appropriate spatial orbitals. To elaborate on these general ideas, the following objectives are playing a crucial role. First, for systems of identical fermions, a solid foundation for particle and for mode/orbital entanglement shall be provided. Based on plausible axioms for fermionic entanglement measures, the flaws of common measures shall be sorted out: The artificial "correlations" due to the antisymmetry of the wave function shall no longer contribute to the particle entanglement. Furthermore, the application of mode/orbital entanglement measures in quantum chemistry must not violate the number parity superselection rule, reflecting the fact that nature never mixes even and odd fermion number states. To simplify their applicability to realistic fermionic systems, bounds and witnesses shall be constructed for those measures.Second, the conflict between energy minimization and fermionic exchange symmetry shall be concretized in the form of an exchange force constructed via reduced density matrix functional theory (RDMFT). For this, I will prove in a constructive way that the fermionic exchange symmetry manifests itself in RDMFT in the form of an effective "potential". The exchange force will then be introduced as the derivative of that potential with respect to the natural occupation numbers.Third, in a comprehensive QC-DMRG study, it shall be systematically verified for quantum chemical and harmonic trap systems that particle and orbital/mode entanglement are both significantly reduced in ground states compared to generic states. The expected strong relation between the reduction of entanglement and the strength of the exchange force shall be verified. To overcome the main limitation of QC-DMRG (recovering dynamic correlations), more general tensor network ansatzes will be exploited, higher virtual orbitals shall be merged to supersites and new insights from the exchange force and RDMFT will be used to improve systematically the choice of the "lattice sites" underlying QC-DMRG. Altogether, this shall eventually pave the way for QC-DMRG-blackbox calculations.
DFG Programme
Independent Junior Research Groups
International Connection
Hungary, Italy, Netherlands, Poland
