Field theories of Kondo-Heisenberg lattices: a quantum Monte Carlo study

• Applicant: Dr. Bimla Danu, Ph.D.
• Subject Area: Theoretical Condensed Matter Physics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 528834426

The Kondo-Heisenberg model describes the physics of magnetic impurities in metals. Here, a number of competing phenomena lead to a very rich phase diagram with exotic phases and phase transitions that occur in various experimental setups. This includes dimensionality mismatch, dissipation induced ordering, Kondo screening versus Ruderman-Kittel-Kasuya-Yosida interaction as well as frustration. A specific example are magnetic adatoms on metallic surfaces, as realized in scanning tunneling microscopy experiments. These systems have the potential to exhibit Kondo breakdown transitions and phases as well as magnetic order-disorder transitions in metallic environments. One can show that the Kondo-Heisenberg model maps onto $U(1)$ lattice gauge theories. This mapping allows to carry out approximation free auxiliary field quantum Monte Carlo simulations. By building on our knowledge of gauge theories we can classify phases and characterize them by measuring Wilson loops, gauge invariant (spinon) correlation functions etc. Aside from this new set of observables, we aim at generating novel phases by adding symmetry allowed flux terms to the action. We foresee that this approach will have many numerical advantages that will allow us to progress in the understanding of phases and phase transitions in these systems. We will also touch on the experimentally relevant issue of de Haas-van Alphen oscillations in Kondo insulators and heavy fermion physics in Moiré superlattices.

• DFG Programme: Research Grants
• Co-Investigator: Professor Dr. Fakher Fakhry Assaad