Entanglement and Surface states of Spin Chains and Semimetals

Quantum systems often do not become ordered even at zero temperature, due to quantum fluctuations.  Surprisingly, there can be phase transitions between two such phases (called "topological phases").  The surface of a topological phase often has surface states that are unique to the phase.  In the interior, the order is hidden.

In this talk, I will first demonstrate that the entanglement spectrum can serve as the order parameter in the one dimensional case.  The central idea is to reduce a one dimensional chain to a zero-dimensional imaginary system which describes the entanglement and is called the "entanglement Hamiltonian." One can then understand the phases of the original spin chain simply by looking at the spectrum of the entanglement Hamiltonian, just as one deduces the properties of atoms from their spectra.

Next I will describe a class of "orderless" materials in three dimensions called Weyl semimetals.  Their carriers satisfy the Weyl equation, which couples spin to the direction of motion.  I will show that these materials have strange surface states called "Fermi arcs" that are half of a Fermi surface, and may be realized among the iridates.