Boundary states of Three Dimensional Topological Order and the Deconfined Quantum Critical Point

Understand

We study the boundary states of the archetypal three-dimensional topological order, i.e.

• the three-dimensional $\mathbb{Z}_2$ toric code.
• There are three distinct elementary types of boundary states that we will consider in this work.
• In the phase diagram that includes the three elementary boundaries there may exist a multi-critical point, which is captured by the so-called deconfined quantum critical point (DQCP) with an "easy-axis" anisotropy.