Determining topological order from a local ground state correlation function


  Zohar Ringel  ,  Yaacov E. Kraus  
Weizmann Institute of Science

Topological order is an elusive quantity to define and measure. It is commonly thought that such order cannot be described by any local order parameter. In this work we show that the Z2 topological order of topological insulators and the Z order of the integer quantum Hall e ffect manifest themselves locally. We describe a procedure for determining these orders from a local equal time ground state correlation function, at any convenient boundary conditions. Our procedure is unaffected by the presence of disorder, and can be naturally generalized to include weak interactions. It may also be implemented to form an efficient and controlled algorithm for distinguishing such phases.