A quantum phase transition is usually achieved by tuning physical parameters
in a Hamiltonian at zero temperature. Here, we demonstrate that the ground
state of a topological phase itself encodes critical properties of its
transition to a trivial phase. To extract this information, we introduce a
partition of the system into two subsystems both of which extend throughout the
bulk in all directions. The resulting bulk entanglement spectrum has a
low-lying part that resembles the excitation spectrum of a bulk Hamiltonian,
which allows us to probe a topological phase transition from a single
wavefunction by tuning either the geometry of the partition or the entanglement
temperature. As an example, this remarkable correspondence between topological
phase transition and entanglement criticality is rigorously established for
integer quantum Hall states.Comment: 5 pages, 2 figures, 3 pages of Supplementary Materia
