Seminarium Fizyki Materii Skondensowanej

The transition from topologically trivial to nontrivial state of a materialusually involves inverting the bulk electronic bands. We show that thefollowing aspects in statistical physics manifest themselves neartopological phase transitions: (1) Despite having no order parameter inthe usual sense, a single-particle correlation function can be defined forany topological lattice models. (2) The correlation length, as well as asusceptibility-like quantity have universal critical exponents thatsatisfy certain scaling laws. (3) The concept of scaling is introduced tojudge topological phase transitions, whose principle is akin to stretchinga messy string to reveal the number of knots it contains.