The theoretical analysis of strongly correlated systems in time-reversal symmetry breaking fields – two-dimensional electron systems in the fractional quantum Hall regime, interacting electrons in quantum dots in an external magnetic field, rotating interacting Bose gases, or atoms and molecules in extreme astrophysical magnetic fields – unavoidably require numerical methods. The exact diagonalization of few-body systems and the variational Monte Carlo evaluation of trial wave functions have been applied with great success in this area in the last decades. More advanced methods, such a diffusion Monte Carlo and path-integral Monte Carlo, could overcome the severe size limitations of exact diagonalization and the unavoidable bias of variational methods. However, technical difficulties arise because both the ground-state wave function and the many-body density matrix become complex-valued.
Nevertheless, diffusion Monte Carlo with phase fixing has been successfully applied to Landau level mixing in fractional quantum Hall states, spin transitions between such states, and strongly correlated states in quantum dots. The application of path-integral methods is sporadic, and highly limited even with the use of large computing resources.
With an eye on possible application in the fractional quantum Hall effect, we are developing quantum Monte Carlo tools both for zero and finite temperature. One can address such issues as the competition of incompressible and compressible states at filling factor 1/2 in wide quantum wells and bilayer systems, the nature and the origin of the fractional quantum Hall state at 5/2, the transition to nematic and charge density wave states, the polarization transition or crossover at both gapped and gapless states driven by the Zeeman energy, or the addition spectra of quantum dots in a magnetic field.
The PhD student gets involved both in the development of Monte Carlo codes and their applications in condensed matter physics and atomic physics.
Reliable background in quantum mechanics and solid-state physics, programming skills, experience with computer algebra softwares.