Entanglement in a simple quantum phase transition

By Tobias J. Osborne, Morten Nielsen. 2002

1,170 citations recorded by the source corpus.

What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems that can be solved. An example of such a system is the one-dimensional infinite-lattice anisotropic XY model. This model is exactly solvable using the Jordan-Wigner transform, and it is possible to calculate the two-site reduced density matrix for all pairs of sites. Using the two-site density matrix, the entanglement of formation between any two sites is calculated for all parameter values and temperatures. We also study the entanglement in the transverse Ising model, a special case of the XY model, which exhibits a quantum phase transition. It is found that the next-nearest-neighbor entanglement (though not the nearest-neighbor entanglement) is a maximum at the critical point. Furthermore, we show that the critical point in the transverse Ising model corresponds to a transition in the behavior of the entanglement between a single site and the remainder of the lattice.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/28bd69baca4a949695820c3a1a93a6f9ad43d945

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. J. Cardy
2. Pasquale Calabrese
3. Frank Verstraete
4. J. I. Cirac
5. Rosario Fazio
6. T. Takayanagi
7. A. Osterloh
8. Luigi Amico

In Atomic and Molecular Physics, and Optics

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

Citations in the corpus

• Form Factors of Branch-Point Twist Fields in Quantum Integrable Models and Entanglement Entropy (2007, background): “At the theoretical level, there has been considerable interest in formulating measures of quantum entanglement [4–8] and applying them to extended quantum systems with many degrees of freedom, such as quantum spin chains [9–17].”
• Entanglement in quantum critical phenomena. (2002, background): “Osterloh et al [12] and Osborne and Nielsen [11] have recently considered the entanglement in the XY spin model, Eq.”
• 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).”
• Adiabatic Quantum Computing (2016, background): “…connection between entanglement entropy and gaps is not nearly as clear in higher dimensional systems, even though entanglement close to quantum phase transitions is a well developed subject (Amico et al., 2008; Osborne and Nielsen, 2002; Osterloh et al., 2002; Vidal et al., 2003; Wu et al., 2004).”
• Area laws in quantum systems: mutual information and correlations. (2007, methodology): “A lot of knowledge has been acquired in Condensed Matter Physics in this direction and is now being used and developed further in the study of entanglement in Quantum Information Theory [1–3].”
• Entanglement in many-body systems (2007, background): “(Osborne and Nielsen, 2002) for the single spin von Neumann entropy).”