  Many topologically nontrivial states of matter possess gapless degrees of
freedom on the boundary, and when these boundary states delocalize into the
bulk, a phase transition occurs and the system becomes topologically trivial.
We show that tensor networks provide a natural framework for analyzing such
topological phase transitions in terms of the boundary degrees of freedom which
mediate it. To do so, we make use of a correspondence between a topologically
nontrivial ground state and its phase transition to a trivial phase established
in [1]. This involved computing the bulk entanglement spectrum (BES) of the
ground state, upon tracing out an extensive subsystem. This work implements BES
via tensor network representations of ground states. In this framework, the
universality class of the quantum critical entanglement Hamiltonian in d
spatial dimensions is either derived analytically or mapped to a classical
statistical model in d + 1 dimensions, which can be studied using Monte Carlo
or tensor renormalization group methods. As an example, we analytically derive
the universality classes of topological phase transitions from the spin-1 chain
Haldane phase and demonstrate that the AKLT wavefunction (and its
generalizations) remarkably contains critical six-vertex (and in general
eight-vertex) models within it.

Strongly Correlated Electrons;High Energy Physics - Theory