C01 E

Numerical simulation of topological and exotic states of quantum matter

Summary

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 exotic 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 the nature of quantum phase transitions in the presence and absence of such topological terms. 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 consider generalized impurity models, aimed at understanding various STM signatures of spin-impurities in metallic environments from the quantum to classical limits. We will also carry out calculations of models of correlated electron systems on hyberbolic lattices. Our aim here is to investigate if novel correlation induced effects emerge in curved spaces. All our calculations will be based on our open source implementation of the auxiliary field quantum Monte Carlo algorithm that we will continue to maintain and develop during this grant period.