Ground states of nanoconfined water chains via density matrix renormalization group and restricted Boltzmann machines

• Applicant: Dr. Tobias Serwatka
• Subject Area: Theoretical Chemistry: Electronic Structure, Dynamics, Simulation
• Term: from 2022 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 503971734

• Final Report Year: 2024

Final Report Abstract

The confinement of small molecules such as water in molecular environments (carbon nanotubes, fullerenes, beryl crystals) offers a route to create new molecular phases with interesting and unusual properties. In this project we developed theoretical methods to investigate the occurrence of new quantum phases of extended systems of small polar molecules, such as H2 O or LiF confined in one dimension. We found that linear water chains embedded in carbon nanotubes form effective two-level systems, where the two quantum states correspond to ordered water chains with opposite net polarization along the chain axis. Hence, by exciting the systems it is possible to switch the polarization. In combination with a strong transverse field it is possible to disturb the axial alignment of the water molecules which results in a vanishing axial polarization. In essence, the system can be considered as a switchable electric dipole, that can be turned on and off, making it an interesting candidate for a quantum nanodevice. In addition, we studied endofullerene chains as another candidate to create ordered quantum phases of molecular rotors. In these systems it is possible to tune the fundamental gap as well as the net polarization by employing different guest molecules and by isotopic substitutions of the trapped molecules. In possible applications, this allows for a better customization of the dipolar switch. By changing the relative arrangement of the cages from a linear to an equilateral zig-zag chain it is even possible to change the nature of the ordered state from ferroelectric to antiferroelectric. In a further project, we were able to show that rotational many-body states, similar to the ones mentioned above, can a) be represented by a recurrent neural network and b) these neural network wave functions can be obtained in a variational procedure. This offers an efficient approach to represent and obtain the ground state of extended systems of dozens and hundreds of rotating molecules. This approach is particularly promising for systems in higher dimensions where the high entanglement renders the usually employed tensor network methods rather inefficient.

Publications

• Ferroelectric water chains in carbon nanotubes: Creation and manipulation of ordered quantum phases. The Journal of Chemical Physics, 157(23).
  Serwatka, Tobias & Roy, Pierre-Nicholas
  
• On the nature of the Schottky anomaly in endohedral water. The Journal of Chemical Physics, 158(12).
  Serwatka, Tobias; Yim, Spencer; Ayotte, Patrick & Roy, Pierre-Nicholas
  
• Optimized basis sets for DMRG calculations of quantum chains of rotating water molecules. The Journal of Chemical Physics, 158(21).
  Serwatka, Tobias & Roy, Pierre-Nicholas
  
• Quantum Criticality and Universal Behavior in Molecular Dipolar Lattices of Endofullerenes. The Journal of Physical Chemistry Letters, 14(24), 5586-5591.
  Serwatka, Tobias & Roy, Pierre-Nicholas
  
• Ground states of planar dipolar rotor chains with recurrent neural networks. The Journal of Chemical Physics, 160(22).
  Serwatka, Tobias & Roy, Pierre-Nicholas
  
• Quantum criticality in chains of planar rotors with dipolar interactions. The Journal of Chemical Physics, 160(10).
  Serwatka, Tobias & Roy, Pierre-Nicholas