MS Seminar (Mathematics - String Theory)

Speaker: Bernard Nienhuis (Amsterdam University)
Title: Entanglement in quantum chains
Date: Thu, Jul 23, 2009, 15:30 - 17:00
Place: Seminar Room at IPMU Prefab. B
Abstract: The concept of entanglement had received renewed attention from its relevance for quantum computation. In condensed matter systems local degrees of freedom are typically highly entangled with each other. How does this entanglement depend on distance or on the number of degrees of freedom?

In this presentation I consider a spin chain, and study the entanglement between a block of spins with the rest of the chain. In order to make quantitative statements we need to quantify the amount of entanglement. A convenient measure of entanglement is the entropy associated with the density matrix of the block of spins. The dependence on the size of the block and of the entire chain is a useful probe into the properties of the ground state, e.g. to determine if the system is at a quantum phase transition.

For a particular choice of the spin chain, we can infer the full dependence of the density matrix on the size of the system. We will present the consequences of this knowledge on the finite
size scaling behavior of the entanglement entropy.