The description of correlation phenomena arising from many-body interactions, such as the electron-electron or the electron-phonon interactions, on a material realistic levels poses an outstandingly hard problem. We aim to solve this by extending and combining high-level (quantum) field theories with state-of-the-art ab initio frameworks. In the following we present an excerpt from our ongoing activities in this field:
Correlated Ground States
Superconductivity, magnetism, or (theoretically predicted) excitonic instabilities are resulting from a complex interplay between the various local and non-local interactions of the electrons and atoms of a material and its structural properties. A realistic description of this requires the combination of ab initio approaches and high-level many-body theory to simultaneously account for the unique properties of each material and the (partially strong) inherent correlations. We successfully applied this combination in the past to uncover the nature of strong electron-phonon interactions in InSe , the interplay of Coulomb repulsion and electron-phonon attraction within the superconducting state of MoS2 , the magnetic properties of CrI3 , and the excitonic transitions in Ta2NiSe5  or nodal-line ZrSiSe [5,6].
 Strong Electron-Phonon Coupling and its Influence on the Transport and Optical Properties of Hole-Doped Single-Layer InSe, A. V. Lugovskoi, M. I. Katsnelson, and A. N. Rudenko, PRL 123, 176401 (2019)
 Interplay of screening and superconductivity in low-dimensional materials, G. Schönhoff, M. Rösner, R. E. Groenewald, S. Haas, and T. O. Wehling, PRB 94, 134504 (2016)
 Orbitally-resolved ferromagnetism of monolayer CrI3, I. V. Kashin, V. V. Mazurenko, M. I. Katsnelson, and A. N. Rudenko, 2D Materials, 7, 2 (2020)
 Nature of Symmetry Breaking at the Excitonic Insulator Transition: Ta2NiSe5, G. Mazza, M. Rösner, L. Windgätter, S. Latini, H. Hübener, A. J. Millis, A. Rubio, and A. Georges, PRL 124, 197601 (2020)
 Excitonic Instability and Pseudogap Formation in Nodal Line Semimetal ZrSiS, A. N. Rudenko, E. A. Stepanov, A. I. Lichtenstein, and M. I. Katsnelson. PRL 120, 216401 (2018)
 Electronic correlations in nodal-line semimetals, Y. Shao, A. N. Rudenko, J. Hu, Z. Sun, Y. Zhu, S. Moon, A. J. Millis, S. Yuan, A. I. Lichtenstein, D. Smirnov, Z. Q. Mao, M. I. Katsnelson & D. N. Basov, Nature Physics 16, 636–641(2020)
Neural quantum states and quantum correlations in realistic systems
Variational Monte Carlo is currently one of the best approaches for tackling frustrated quantum systems. We develop and improve algorithms  combining Deep Learning with Variational Monte Carlo methods. This is a new field, but it has already provided some interesting insights into the wavefunction sign structure of frustrated magnets  which might lead to deeper connections to fundamental problems such as the "sign problem" or mathematical definition of complexity.
 NetKet: A machine learning toolkit for many-body quantum systems, G. Carleo, K. Choo, D. Hofmann, J. E. Smith, T. Westerhout, F. Alet, ... , and M. Mauri, SoftwareX, 10, 100311 (2019)
 Generalization properties of neural network approximations to frustrated magnet ground states, T. Westerhout, N. Astrakhantsev, K. S. Tikhonov, M. I. Katsnelson, and A. A. Bagrov, Nature comm., 11, 1 (2020)
Novel Heterojunctions from Coulomb Engineering
Ground state properties are very often influenced by the Coulomb interaction. A famous example is the band gap of silicon, which is underestimated in conventional density functional theory calculations, but (approximately) correctly described within GW theory. This influence is especially strong in the semi-conducting transition metal dichalcogenides monolayers MoS2, MoSe2, WS2, and WSe2. At the same time the dielectric environment, such as a substrate, can efficiently screen the Coulomb interaction of these layered materials . Thus, the environment of layered semiconductors can be utilized to control their band structures. We employed this concept to systematically study how the band structure as well as excitonic absorption properties of these transition metal dichalcogenides are affected in experimental setups [2,3] and proposed a novel type of heterostructure from spatially structured substrate [4,5,6].
 Wannier function approach to realistic Coulomb interactions in layered materials and heterostructures, M. Rösner, E. Şaşıoğlu, C. Friedrich, S. Blügel, and T. O. Wehling, PRB 92, 085102 (2015)
 Influence of Excited Carriers on the Optical and Electronic Properties of MoS, A. Steinhoff, M. Rösner, F. Jahnke, T. O. Wehling, and C. Gies, Nano Lett. 14, 7, 3743 (2014)
 Exciton fission in monolayer transition metal dichalcogenide semiconductors, A. Steinhoff, M. Florian, M. Rösner, G. Schönhoff, T. O. Wehling & F. Jahnke, Nature Comm., 8, 1166 (2017)
 Two-Dimensional Heterojunctions from Nonlocal Manipulations of the Interactions, M. Rösner, C. Steinke, M. Lorke, C. Gies, F. Jahnke, and T. O. Wehling, Nano Lett. 16, 4, 2322 (2016)
 Coulomb-Engineered Heterojunctions and Dynamical Screening in Transition Metal Dichalcogenide Monolayers, C. Steinke, T. O. Wehling, and M. Rösner, arXiv:1912.10430
 Rigid Band Shifts in Two-Dimensional Semiconductors through External Dielectric Screening, L. Waldecker, A. Raja, M. Rösner, C. Steinke, A. Bostwick, R. J. Koch, C. Jozwiak, T. Taniguchi, K. Watanabe, E. Rotenberg, T. O. Wehling, and T. F. Heinz, PRL 123, 206403 (2019)
LDA+DMFT, Dual Fermions, and Dual Bosons
Dynamical mean-field theory (DMFT) has become the standard approximation for strongly correlated fermionic systems. In finite dimension, DMFT is an approximation that neglects non-local correlations, which are, however, of crucial importance for the description of collective excitations and in the presence of long-range electron-electron interactions. In order to overcome this approximation we developed the Dual Fermion (DF)  and Dual Boson (DB)  approaches. The latter became one of the most advanced techniques that can accurately describe various material properties by considering local electronic correlations exactly via the (extended) DMFT and nonlocal ones diagrammatically. We demonstrated that the DB scheme is free from double-counting problems and many existing approaches, such as GW+EDMFT and TRILEX, can be derived analytically as a certain approximation of the DB method . The performance of our theory has been tested in prediction of phase transitions of the extended Hubbard model. For instance, we showed that the DB approach detects the phase boundary between the Fermi liquid and charge ordered phases in a perfect agreement with much more time consuming dynamical cluster approximation methods. The DB approach also allowed us to study for the first time plasmonic excitations in the presence of strong local correlation  and the competition of strong non-local Coulomb interactions with electron-phonon interactions in NbS2 within an ab initio setting .
 Dual fermion approach to nonlocal correlations in the Hubbard model, A. N. Rubtsov, M. I. Katsnelson, and A. I. Lichtenstein, PRB 77, 033101 (2008)
 Dual boson approach to collective excitations in correlated fermionic systems, A. N. Rubtsov, M. I. Katsnelson, and A. I. Lichtenstein, Ann. Phys. (NY) 327, 1320 (2012)
 From local to nonlocal correlations: The Dual Boson perspective, E. A. Stepanov, A. Huber, E. G. C. P. van Loon, A. I. Lichtenstein, and M. I. Katsnelson, PRB 94, 205110 (2016)
 Plasmons in Strongly Correlated Systems: Spectral Weight Transfer and Renormalized Dispersion, E. G. C. P. van Loon, H. Hafermann, A. I. Lichtenstein, A. N. Rubtsov, and M. I. Katsnelson, PRL 113, 246407 (2014)
 Competing Coulomb and electron–phonon interactions in NbS2, E. G. C. P. van Loon, M. Rösner, G. Schönhoff, M. I. Katsnelson, and T. O. Wehling, npj Quantum Mat., 3, 32 (2018)