Scaling of Entanglement close to a Quantum Phase Transition

Classical phase transitions occur when a physical system reaches a state below a critical temperature characterized by macroscopic order(1). Quantum phase transitions occur at absolute zero; they are induced by the change of an external parameter or coupling constant(2), and are driven by quantum fluctuations. Examples include transitions in quantum Hall systems(3), localization in Si-MOSFETs (metal oxide silicon field-effect transistors; ref. 4) and the superconductor-insulator transition in two-dimensional systems(5,6). Both classical and quantum critical points are governed by a diverging correlation length, although quantum systems possess additional correlations that do not have a classical counterpart. This phenomenon, known as entanglement, is the resource that enables quantum computation and communication(8). The role of entanglement at a phase transition is not captured by statistical mechanics-a complete classification of the critical many-body state requires the introduction of concepts from quantum information theory(9). Here we connect the theory of critical phenomena with quantum information by exploring the entangling resources of a system close to its quantum critical point. We demonstrate, for a class of one-dimensional magnetic systems, that entanglement shows scaling behaviour in the vicinity of the transition point.