Entanglement in Disordered Systems at Criticality

Entanglement is a physical resource of a quantum system just like mass, charge or energy. Moreover it is an essential tool for many purposes of nowadays quantum information processing, e.g. quantum teleportation, quantum cryptography or quantum computation. In this work we investigate an extended system of N qubits. In our system a qubit is the absence or presence of an electron at a site of a tight-binding system. Several measures of entanglement between a given qubit and the rest of the system and also the entanglement between two qubits and the rest of the system is calculated in a one-electron picture in the presence of disorder. We invoke the power law band random matrix model which even in one dimension is able to produce multifractal states that fluctuate at all length scales. The concurrence, the tangle and the entanglement entropy all show interesting scaling properties.