Ari Turner, University of Amsterdam
Entanglement (as in the Einstein, Podolsky, Rosen paradox) is a major distinctive feature of quantum mechanics. To demonstrate the existence of entanglement in the simplest way, entangling the spins of photons, one has to be very careful in preparing the states, as the entanglement is fragile. However, entanglement is present in the ground state of every many body system. In particular it plays an important role in a type of phase called a "topological phase." We will illustrate this with the case of spin chains.
Often, spin chains do not have any long range order, because of quantum mechanical fluctuations. Surprisingly, there can be phase transitions between two such phases, which suggests the existence of a hidden order (which has been called "topological order").
In this talk, I demonstrate that the entanglement spectrum can serve as an order parameter for these unusual transitions. 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.
The entanglement spectrum has also the potential for clarifying properties of quantum phases without order in higher dimensions, as exhibited by topological insulators.