Dynamical Gauge Fields and Fractional Chern Insulators

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We investigate strongly interacting states of quantum matter interacting with dynamical gauge fields. One part of the project focuses on fractional Chern insulators, in which dynamical gauge fields can lead to flux-attachment and to the formation of weakly interacting composite fermions. The second part of the project is concerned with the simplest instant of a lattice gauge theory (LGT) - an Ising or Z2 LGT - coupled to a matter field. Both system are now within reach of ultracold atom experiments in optical lattices, thanks to the capabilities achieved by resonant lattice modulations. Here we will study theoretically various aspects of these models, which allow on one hand to connect to long-standing problems involving strongly correlated electrons and which are of immediate experimental relevance on the other hand. These include (A) the theoretical description of fractional Chern insulators, with special emphasis on the role of lattice effects and the bosonic Pfaffian state at unit magnetic filling hosting non-Abelian excitations; (B) The study of Z2 LGTs coupled to matter fields and their phase diagram in quasi-one dimensional multi-leg ladder geometries; And (C) dynamical probes of such strongly correlated states of matter, with special emphasis on spectroscopic probes of the underlying topological properties. Our main tool will be state-of-the-art DMRG simulations, extended to time-dependent calculations and two-dimensional systems. Additionally, we will perform physically motivated variational calculations.