Numerical simulations of topological and exotic states of quantum matter

• Applicant: Professor Dr. Fakher Fakhry Assaad
• Subject Area: Theoretical Condensed Matter Physics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 530989922

The goal of our research is to use numerical methods to unravel correlation driven effects in fermionic systems. Topology is at the center of our understanding of phases and phase transitions. For example it is known that in 1+1 dimensions, the physics of half-integer and integer spin chains differ by the presence or absence of a topological term in the action. This notion can be generalized to 2+1 dimensions. One of the aims of our research is to investigate a model in 2+1 dimensions where topological terms, that emerge in the vicinity of quantum phase transitions, can be switched on and off as a function of a model parameter. We will pursue our work on the electron-phonon interactions and in particular concentrate on a symmetry allowed generalization of the Su-Schrieffer-Heeger model. Here we will use a novel approach in which we can integrate out the phonons. We aim to understand the physics of this model from the assisted-hopping regime, where it maps onto Z2 lattice gauge theories, to the regime where the modulation of the hopping is small as compared to the hopping itself. These two main subjects will be supplemented by research along two other directions. We will carry out calculations of models of correlated electron systems on hyperbolic lattices. Our aim here is to investigate if novel correlation induced effects emerge in curved spaces. Phonons in thermal transport play a pivotal role. We aim to use our advances in simulations of the Su-Schrieffer-Heeger hamiltonian to investigate thermal transport in phases and across phase transitions. All our numerically exact calculations on finite lattices will be carried out with our open source implementation of the auxiliary field quantum Monte Carlo algorithm.

• DFG Programme: Research Grants