Description
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, fractional quantum Hall
states, and Chern-Simons theories will be discussed.
