Master's project: Fermionic neural quantum states

A central objective of our work is the advancement of numerical simulation techniques based on neural quantum states (NQS). The underlying idea of this approach is to tackle the quantum curse of dimensionality by exploiting the proven merit of artificial neural networks for dealing with high-dimensional data. This new numerically exact technique can overcome existing limitations of established computational methods. Thereby, it will open up intriguing physical regimes for numerical simulation, such as correlated electrons, which are confined to two spatial dimensions.

The goal of this project is investigate a disorder-driven insulator-superconductor transition. Generally, disorder in metals leads to a localization of the electronic wave function in the system and thus, to the transition from a conductor to an insulator. Similarly, it has been suggested that disorder in superconducting systems can drive the breakdown of the superconducting phase and the emergence of an insulating phase. A full simulation of such situations including all quantum correlations, however, still open.

As a rather young numerical approach, the NQS method is still under ongoing development and significant challenges have been identified when tackling model systems of interacting Fermions. Therefore, the first objective of this project will be to explore new ideas to overcome some of the existing challenges.

If you are interested in this project, don’t hesitate to get in touch.

Notice: This project is suited for you, if you pursue a Master’s degree in physics.

References

  • G. Carleo and M. Troyer, “Solving the quantum many-body problem with artificial neural networks”, Science 355, 602 (2017)
  • M. Bukov, M. Schmitt, M. Dupont, “Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape”, SciPost Phys. 10, 147 (2021)
  • M. Stosiek, B. Lang, and F. Evers, “Self-consistent-field ensembles of disordered Hamiltonians: Efficient solver and application to superconducting films”, Phys. Rev. B 101, 144503 (2020)
  • B. Sacépé, M. Feigel’man , and T. M. Klapwijk, “Quantum breakdown of superconductivity in low-dimensional materials”, Nat. Phys. 16, 734–746 (2020)