Publications

Publications and recent preprints

1. Refining ensemble N-representability of one-body density matrices from partial information (2025) 

     Julia Liebert, Anna O. Schouten, Irma Avdic, Christian Schilling, David A. Mazziotti
     New J. Phys. 27, 124511

2. Solving one-body ensemble N-representability problems with spin (2025) 

Julia Liebert, Federico Castillo, Jean-Philippe Labbé, Tomasz Maciazek, Christian Schilling

     Quantum 9, 1921 

3. Spin adaptation of the cumulant expansions of reduced density matrices (2025) 

     Julia Liebert, Christian Schilling, David A. Mazziotti
     arXiv:2505.16989                                                                                   

4. A toolbox of spin-adapted generalized Pauli constraints (2025)
   Julia Liebert, Yannick Lemke, Murat Altunbulak, Tomasz Maciazek, Christian Ochsenfeld,  Christian Schilling
   Phys. Rev. Research 7, 023247 

5. From Entanglement to Bonds: Chemical Bonding Concepts from Quantum Information Theory (2025)
   Lexin Ding, Eduard Matito, Christian Schilling
   arXiv:2501.15699

6. How to Incorporate Symmetries in Functional Theories (2025) 

Julia Liebert, Tomasz Maciazek, Christian Schilling

Submitted

7. Functional theory for quantum phase transitions (2025)
   Martin Uttendorfer, Julia Liebert, Christian Schilling
   Submitted 

8. A Spin-Faithful and Irreducible One-Matrix Functional Theory (2025)
   Julia Liebert, T. Maciazek, Christian Schilling
   Submitted

9. Unveiling Intrinsic Many-Body Complexity by Compressing Single-Body Triviality (2024)
   Ke Liao, Lexin Ding, Christian Schilling
   J. Phys. Chem. Lett. 15, 6782

10. What can Quantum Information Theory Offer to Quantum Chemistry? (2024)
    Damiano Aliverti-Piuri, Kaustav Chatterjee, Lexin Ding, Ke Liao, Julia Liebert, Christian Schilling
    Faraday Discuss. 254, 76

11. Ground and Excited States from Ensemble Variational Principles (2024)
    Lexin Ding, Cheng-Lin Hong, Christian Schilling
    Quantum 8, 1525 

12. Quantum Information-Assisted Complete Active Space Optimization (QICAS) (2023)
    Lexin Ding, Stefan Knecht, Christian Schilling
    J. Phys. Chem. Lett. 14, 49, 11022

13. Refining the weighted subspace-search variational quantum eigensolver: Compression of ansätze into a single pure state and optimization of weights (2023)
    Cheng-Lin Hong, Luis Colmenarez, Lexin Ding, Carlos L. Benavides-Riveros, Christian Schilling
    arXiv:2306.11844

14. Physical Entanglement Between Localized Orbitals (2023)
    Lexin Ding, Gesa Dünnweber, Christian Schilling
    Quantum Sci. Technol. 9, 015005

15. An effective solution to convex 1-body N-representability (2023)
    Federico Castillo, Jean-Philippe Labbé, Julia Liebert, Arnau Padrol, Eva Philippe, Christian Schilling
    Ann. Henri Poincaré 24, 2241

16. Refining and relating fundamentals of functional theory (2023)
    Julia Liebert, Adam Y. Chaou, Christian Schilling
    J. Chem. Phys. 158, 214108

17. Deriving density-matrix functionals for excited states (2023)
    Julia Liebert, Christian Schilling
    SciPost Phys. 14, 120

18. An exact one-particle theory of bosonic excitations: From a generalized Hohenberg-Kohn theorem to convexified N-representability (2023)
    Julia Liebert, Christian Schilling
    New J. Phys. 25, 013009

19. 1-matrix functional for long-range interaction energy of two hydrogen atoms (2023)
    Jerzy Cioslowski, Christian Schilling, Rolf Schilling
    J. Chem. Phys. 158, 084106 (Editor's Pick)

20. Quantum correlations in molecules: From quantum resourcing to chemical bonding (2023)
    Lexin Ding, Stefan Knecht, Zoltán Zimborás, Christian Schilling
    Quantum Sci. Technol. 8, 015015

21. Quantifying Electron Entanglement Faithfully (2022)
    Lexin Ding, Zoltán Zimborás, Christian Schilling
    arXiv:2207.03377

22. Comment on "Self-Consistent-Field Method for Correlated Many-Electron Systems with an Entropic Cumulant Energy" (2022)
    Lexin Ding, Julia Liebert, Christian Schilling
    arXiv:2202.05532

23. Excitations of Quantum Many-Body Systems via Purified Ensembles: A Unitary-Coupled-Cluster-based Approach (2022)
    Carlos L. Benavides-Riveros, Lipeng Chen, Christian Schilling, Sebastián Mantilla, Stefano Pittalis
    Phys. Rev. Lett. 129, 066401 (Editor's Suggestion)

24. Foundation of one-particle reduced density matrix functional theory for excited states (2021)
    Julia Liebert, Frederico Castillo, Jean-Philippe Labbé, Christian Schilling
    J. Chem. Theory Comput. 18, 1, 124

25. Introduction to Fermionic Entanglement and Correlation (2021)
    Christian Schilling
    Proceedings of the Autumn School Simulating Correlations with Computers, Vol. 11, edited by E. Pavarini and E. Koch, Jülich, Germany

26. Ensemble reduced density matrix functional theory for excited states and hierarchical generalization of Pauli's exclusion principle (2021)
    Christian Schilling, Stefano Pittalis
    Phys. Rev. Lett. 127, 023001

27. Fermionic systems for quantum information people (2021)
    Szilárd Szalay, Zoltán Zimborás, Mihály Máté, Gergely Barcza, Christian Schilling, Örs Legeza
    J. Phys. A: Math. Theor. 54, 393001

28. Functional Theory for Bose-Einstein Condensates (2021)
    Julia Liebert, Christian Schilling
    Phys. Rev. Research 3, 013282

29. How creating one additional well can generate Bose-Einstein condensation (2021)
    Mihály Máté, Örs Legeza, Rolf Schilling, Mason Yousif, Christian Schilling
    Commun. Phys. 4, 29

30. Concept of orbital entanglement and correlation in quantum chemistry (2021)
    Lexin Ding, Sam Mardazad, Sreetama Das, Szilárd Szalay, Ulrich Schollwöck, Zoltán Zimborás, Christian Schilling
    J. Chem. Theory Comput. 17, 1, 79

31. Reduced Density Matrix Functional Theory for Bosons (2020)
    Carlos L. Benavides-Riveros, Jakob Wolff, Miguel A. L. Marques, Christian Schilling
    Phys. Rev. Lett. 124, 180603

32. Correlation paradox of the dissociation limit: A quantum information perspective (2020)
    Lexin Ding, Christian Schilling
    J. Chem. Theory Comput. 16, 4159

33. Implications of pinned occupation numbers for natural orbital expansions. II: Rigorous derivation and extension to non-fermionic systems (2020)
    Tomasz Maciazek, Adam Sawicki, David Gross, Alexandre Lopes, Christian Schilling
    New J. Phys. 22, 023002

34. Implications of pinned occupation numbers for natural orbital expansions. I: Generalizing the concept of active spaces (2020)
    Christian Schilling, Carlos L. Benavides-Riveros, Alexandre Lopes, Tomasz Maciazek, Adam Sawicki
    New J. Phys. 22, 023001

35. Diverging exchange force and the form of density matrix functionals (2019)
    Christian Schilling, Rolf Schilling
    Phys. Rev. Lett. 122, 013001

36. Communication: Relating the pure and ensemble density matrix functional (2018)
    Christian Schilling
    J. Chem. Phys. 149, 231102

37. Role of the pair potential for the saturation of generalized Pauli constraints (2018)
    Örs Legeza, Christian Schilling
    Phys. Rev. A 97, 052105

38. Generalized Pauli constraints in small atoms (2018)
    Christian Schilling, Murat Altunbulak, Stefan Knecht, Alexandre Lopes, James D. Whitfield, Matthias Christandl, David Gross, Markus Reiher
    Phys. Rev. A 97, 052503

39. Reconstructing quantum states from single-party information (2017)
    Christian Schilling, Carlos Benavides-Riveros, Peter Vrana
    Phys. Rev. A 96, 052312

40. Universal upper bounds on the Bose-Einstein condensate and the Hubbard star (2017)
    Felix Tennie, Vlatko Vedral, Christian Schilling
    Phys. Rev. B 96, 064502

41. Relating correlation measures: the importance of the energy gap (2017)
    Carlos Benavides-Riveros, Christian Schilling, Nektarios Lathiotakis, Miguel Marques
    Phys. Rev. A 95, 032507

42. Influence of the fermionic exchange symmetry beyond Pauli's exclusion principle (2016)
    Felix Tennie, Vlatko Vedral, Christian Schilling
    Phys. Rev. A 95, 022336

43. Pinning of Fermionic Occupation Numbers: Higher Spatial Dimensions and Spin (2016)
    Felix Tennie, Vlatko Vedral, Christian Schilling
    Phys. Rev. A 94, 012120

44. Pinning of Fermionic Occupation Numbers: General Concepts and One Spatial Dimension (2016)
    Felix Tennie, Daniel Ebler, Vlatko Vedral, Christian Schilling
    Phys. Rev. A 93, 042126

45. Natural Extension of Hartree-Fock through extremal 1-fermion information: Overview and application to the lithium atom (2016)
    Carlos Benavides-Riveros, Christian Schilling
    Z. Phys. Chem. 230, 703-717

46. Number-parity effect for confined fermions in one dimension (2016)
    Christian Schilling, Rolf Schilling
    Phys. Rev. A 93, 021601, Rapid Communication

47. Hubbard model: Pinning of occupation numbers and role of symmetries (2015)
    Christian Schilling
    Phys. Rev. B 92, 155149

48. Quasipinning and its relevance for N-Fermion quantum states (2015)
    Christian Schilling
    Phys. Rev. A 91, 022105

49. Duality of reduced density matrices and their eigenvalues (2014)
    Christian Schilling, Rolf Schilling
    J. Phys. A 47, 415305

50. Natural Orbitals and Occupation Numbers for Harmonium: Fermions versus Bosons (2013)
    Christian Schilling
    Phys. Rev. A 88, 042105

51. Pinning of Fermionic Occupation Numbers (2013)
    Christian Schilling, David Gross, Matthias Christandl
    Phys. Rev. Lett. 110, 040404
    With Editors' Suggestion and Viewpoint in Physics

Proceedings and other contributions

52. Stochastic and low-scaling techniques: general discussion (2024)
    Ali Alavi, ... Christian Schilling, ... Martijn A. Zwijnenburg (46 contributors)
    Faraday Discuss. 451, 191

53.  Novel perturbative and variational methods for stronger correlations: general discussion (2024)
    Vibin Abraham, ... Christian Schilling, ... Dominika Zgid (30 contributors)
    Faraday Discuss. 254, 191

54. The Quantum Marginal Problem (2014)
    Christian Schilling
    Mathematical Results in Quantum Mechanics 10, 165, World Scientific

Software codes and packages

55. MEAO: A package for electronic structure analysis based on maximally entangled atomic orbitals (2025)

Lexin Ding, Eduard Matito, Christian Schilling

available upon request, soon to be released on https://github.com/schilling-group

56. QIO: Quantum information-assisted orbital optimization package (2024)

Lexin Ding, Ke Liao, Christian Schilling

https://github.com/schilling-group