Topological order: new states and new probes
This event is part of the Biophysics/Condensed Matter Seminar Series.
Since the identification of quantum Hall states as topological states of matter, the search for new topological states of matter has been a central endeavour. I will present the composite fermion theory of fractional quantum Hall states in the Hofstadter model of interacting particles on a lattice exposed to a (synthetic) magnetic field , providing the numerical evidence for Chern insulators [1,2]. In this model, new types of fractional quantum Hall states can be formed due to the presence of higher Chern number bands in the single-particle spectrum [2,3].
Another crucial question remains how to best probe topologically ordered phases in experiment, besides macroscopic properties such as quantised Hall conductance. I will discuss the topological marker  as an interesting local probe for topological order, and discuss how to use the marker to probe the critical properties of topological phase transitions, as well as its non-equilibrium dynamics after a quantum quench through the transition . Finally, I will show how the topological marker can be inferred from measurements of the single-particle density matrix .
1.Möller, G. & Cooper, N. R. Composite Fermion Theory for Bosonic Quantum Hall States on Lattices. Phys. Rev. Lett. 103, 105303 (2009). 2.Möller, G. & Cooper, N. R. Fractional Chern Insulators in Harper-Hofstadter Bands with Higher Chern Number. Phys. Rev. Lett. 115, 126401 (2015). 3.Andrews, B. & Möller, G. Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number |C|>1. Phys. Rev. B 97, 035159 (2018). 4.Bianco, R. & Resta, R. Mapping topological order in coordinate space. Phys. Rev. B 84, 241106 (2011). 5.Caio, M. D., Möller, G., Cooper, N. R. & Bhaseen, M. J. Topological Marker Currents in Chern Insulators, Nature Physics 315, 1 (2019).