Condensed Matter Seminar

Eduardo Fradkin
University of Illinois, Urbana-Champaign

Thursday, February 21, 2008
1:00 pm in SPL 52

Entanglement Entropy at two dimensional quantum critical points and 2D topological fluids: can you hear the shape of Schrödinger's cat?

Abstract: The entanglement entropy of a pure quantum state of a bipartite system is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. Critical ground states of local Hamiltonians in one dimension have entanglement that diverges logarithmically in the subsystem size, with a universal coefficient that is is related to the central charge of the associated conformal field theory. In this talk I will discuss the extension of these ideas to two dimensional systems, either at a special quantum critical point or in a topological phase. We find the entanglement entropy for a standard class of z = 2 quantum critical points in two spatial dimensions with scale invariant ground state wave functions: in addition to a nonuniversal "area law" contribution proportional to the size of the boundary of the region under observation, there is generically a universal logarithmically divergent correction. This logarithmic term is completely determined by the geometry of the partition into subsystems and the central charge of the field theory that describes the equal-time correlations of the critical wavefunction. On the other hand, in a topological phase there is no such logarithmic term but instead a universal constant term. We will discuss the connection between this universal entanglement entropy and the nature of the topological phase. The application of these ideas to quantum dimer models and fractional quantum Hall states will be discussed.