Scaling of entanglement close to a quantum phase transition

By A. Osterloh, Luigi Amico, Giuseppe Falci, Rosario Fazio. Nature, 2002

1,465 citations recorded by the source corpus.

Classical phase transitions occur when a physical system reaches a state below a critical temperature characterized by macroscopic order. Quantum phase transitions occur at absolute zero; they are induced by the change of an external parameter or coupling constant, and are driven by quantum fluctuations. Examples include transitions in quantum Hall systems, localization in Si-MOSFETs (metal oxide silicon field-effect transistors; ref. 4) and the superconductor–insulator transition in two-dimensional systems. 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. 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. 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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/001e63e034ac2e4db176f88f6b299fbcf7edefaf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Pasquale Calabrese
2. J. Cardy
3. Frank Verstraete
4. T. Takayanagi
5. J. I. Cirac
6. Rosario Fazio
7. Andrew J. Daley
8. Tameem Albash

In Atomic and Molecular Physics, and Optics

1. Pasquale Calabrese
2. J. Cardy
3. Frank Verstraete
4. J. Dubail
5. T. Takayanagi
6. J. I. Cirac
7. Andrew J. Daley
8. Rosario Fazio

In Electrical and Electronic Engineering

1. J. Cardy
2. Daniel A. Lidar
3. Tameem Albash
4. J. I. Cirac

Citations in the corpus

• Evolution of entanglement entropy in one-dimensional systems (2005, background): “In the last few years several measures of entanglement have been proposed [1,2], and have been calculated (analytically in the simplest instances, otherwise numerically) in the ground state of several many-body systems.”
• Quantum simulations with cold trapped ions (2009, background): “…the connection between entanglement on the one hand, and static and dynamic properties of many-body systems on the other hand, for instance, near quantum phase transitions has attracted much interest (e.g., [Osterloh et al. 2002, Amicoet al. 2008, Plenio & Virmani 2007] and references therein).”
• The classical-quantum boundary for correlations: Discord and related measures (2011, background): “It is known that the nonanalyticity of energy is manifested in terms of entanglement between the nearest and the next-nearest neighbors at a critical point (Osborne and Nielsen, 2002; Osterloh et al., 2002).”