Christian Schilling

Quantum Information Theory & Quantum Many-Body Physics

Ludwig-Maximilians-Universität München

Arnold-Sommerfeld Center for Theoretical Physics

Theresienstr. 37

80333 Munich

+49 89 2180 4594

c.schilling[at]physik.uni-muenchen.de

Research Webpage

The beauty of theoretical physics makes our daily work with pencil and paper an inspiring endeavour.

Description

Research focus: concept of fermionic entanglement, reduced density matrices, ground state methods.

Our group is carrying out research at the interface of Quantum Information Theory and Quantum Many-Body Physics. We resort to analytic approaches partly complemented/guided by computational studies to gain universal insights into interacting quantum many-body systems.

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Foundation of Fermionic Correlation and Entanglement

Entanglement and correlation are some of the most fascinating concepts of modern physics. Yet, in the context of indistinguishable particles a solid foundation is still lacking. Inspired by resource theory we elaborate on the two most natural definitions of fermion entanglement and correlation. The first one describes how close our N-fermion state is to the set of particle-uncorrelated “Slater determinant”-states. The second one refers to the 2nd quantization and describes how strongly orbitals (rather than particles) are entangled and correlated. Corresponding entanglement and correlation measures follow from the underlying geometric picture of quantum states. We believe that the concept of such particle and orbital correlation provides a concise and operationally meaningful alternative to the concept of static and dynamic correlations, as used in chemistry and materials science.

Ground State Problem

Based on our interdisciplinary background and expertise in quantum many-body physics, quantum information theory and mathematical physics, we are working on a more systematic and more effective approach to the notoriously difficult ground state problem. To be more specific, let us recall that in realistic quantum many-body systems the electrons interact only by two-body forces and the interaction always exhibits some form of spatial locality. The consequences of exactly those two fundamental features of realistic systems shall be explored, quantified and exploited. In particular, we plan to show from a quite general perspective that it is the universal conflict between energy minimization and fermionic exchange symmetry which together with those two fundamental features enforces a significant reduction of the particle correlations and orbital correlations in ground states compared to generic quantum states.

Density Matrix Renormalization Group (DMRG) ansatz in quantum chemistry

The remarkable success of DMRG in lattice systems is based on the reduced spatial entanglement following from the locality of the interaction. Quite in contrast, the recent success of DMRG in quantum chemical systems is rather astonishing: Why should the respective molecular Hamiltonians exhibit any local structure on the underlying artificial lattice formed by the molecular orbitals? Our main goal is to explain the emergence of a local structure by tracing it back to a deeper origin, namely the universal conflict between energy minimization and fermionic exchange symmetry in systems of continuously confined fermions. Furthermore, limitations and shortcomings of the recent version of DMRG in quantum chemistry shall be overcome, such as its inability to recover dynamic correlations with sufficiently high precision.

Reduced Density Matrix Functional Theory

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Reduced density matrix functional theory (RDMFT) is expected to replace in the future density functional theory as the workhorse of modern electronic structure calculations in physics, chemistry and materials science. By using concise tools from quantum information theory and mathematical physics we are working on a solid foundation for RDMFT. In particular, we are interested in deriving universal features of the exact functional. For instance, we recently succeeded in proving that the fermionic exchange symmetry manifests itself within RDMFT in the form of a universal “fermionic exchange force”, preventing fermionic occupation numbers from ever reaching the exact values 0 and 1. Its bosonic analogue, a “Bose Einstein Condensation”- force explains the absence of complete condensation in nature and in that sense provides a fundamental explanation for quantum depletion.

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