The emergence of quantum spin liquid phases of matter from local spin interactions is of fundamental interest in contemporary condensed matter physics. While several exactly solvable toy models for quantum spin liquids have been proposed and investigated, the theoretical study of (frustrated) spin systems with more realistic interactions relies on numerical simulations. We give a short overview of numerical methods to identify topologically ordered states and focus on the method of using numerical exact diagonalization in combination with variational wave functions. We present recent advances of the method and show, how this approach has been applied to identify certain chiral spin liquids in two-dimensional frustrated Heisenberg models.
This seminar is organized in the framework of the PSI2 program "Topological phases of matter: from the quantum Hall effect to spin liquids" (Topmat)