Entanglement and correlation functions following a local quench: a conformal field theory approach

By Pasquale Calabrese, J. Cardy. 2007

344 citations recorded by the source corpus.

We show that the dynamics resulting from preparing a one-dimensional quantum system in the ground state of two decoupled parts, then joined together and left to evolve unitarily with a translational invariant Hamiltonian (a local quench), can be described by means of quantum field theory. In the case when the corresponding theory is conformal, we study the evolution of the entanglement entropy for different bipartitions of the line. We also consider the behavior of one- and two-point correlation functions. All our findings may be explained in terms of a picture, that we believe to be valid more generally, whereby quasiparticles emitted from the joining point at the initial time propagate semiclassically through the system.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/67286390a4820ad6066f320503aacbba205b5653

How researchers see this paper

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

In Atomic and Molecular Physics, and Optics

1. R. Myers
2. T. Takayanagi
3. Thomas Hartman
4. Pasquale Calabrese
5. E. Tonni
6. J. Maldacena
7. V. Hubeny
8. J. Dubail

In Condensed Matter Physics

1. T. Takayanagi
2. Pasquale Calabrese
3. J. Cardy
4. E. Tonni
5. J. Dubail
6. Thomas Hartman
7. A. Allais
8. R. Myers

In Statistical and Nonlinear Physics

1. R. Myers
2. T. Takayanagi
3. S. Raju
4. D. Harlow
5. Thomas Hartman
6. V. Hubeny
7. H. Chen
8. D. Stanford

Citations in the corpus

• Holographic entanglement entropy from 2d CFT: heavy states and local quenches (2014, methodology): “2 by commenting on the relation of these local quenches to the well-known ones studied in [37, 38], and holographically in [35,39,40].”
• Quantum trajectories and open many-body quantum systems (2014, background): “In general, jump operators that are local in space, and so provide a local quench for the system should lead to a slower entanglement growth than global quenches [268], which should favour the use of quantum trajectories methods to describe the resulting dynamics.”
• Holographic evolution of the mutual information (2011, methodology): “These situations have been studied for two dimensional systems by employing conformal field theory techniques and spin chains models [25, 26, 27, 28, 29].”
• Entanglement entropy in quantum impurity systems and systems with boundaries (2009, background): “Recently there has been some very interesting work on time-dependent entanglement entropy following a local quench, which also involves systems with quantum impurities [35–38].”
• Information flow in black hole evaporation (2019, methodology): “It remains an open problem to apply a more rigorous analysis of the quench, à la [21–23], to the AEMZ model.”
• Entanglement entropy and conformal field theory (2009, methodology): “It is easy to perform the mapping, continuing to real time τ → it , and for t we have [114] 〈Tn(iτ)〉 = c̃n [ π 4 1 t sin(πt/2 ) ]dn .”
• Entanglement entropy of two disjoint intervals in conformal field theory (2009, background): “Instead the function F̃n(x) affects some results in [33] for local quantum quenches, that however are easily corrected using the formulae for general four-point correlation functions presented in the same paper.”
• Holographic local quenches and entanglement density (2013, background): “By comparing this estimation of the entanglement entropy in CFTs with (5.4), we can speculate that the number of disentanglers in a bond is roughly approximated by l2 ·n(l, ξ, t) in more general tensor networks which do not correspond to ground states of CFTs.”
• The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole (2019, result): “This approach gives an alternative route to previous results on local quantum quenches [40–42].”
• Conformal Field Theory for Inhomogeneous One-dimensional Quantum Systems: the Example of Non-Interacting Fermi Gases (2016, background): “This is somehow reminiscent of a similar anomalous scaling found in local quenches [59] and it is unclear whether there is a connection between the two.”
• Quantum quenches in 1  +  1 dimensional conformal field theories (2016, methodology): “[187] also the entanglement of a finite interval (both on one side or across the cutting point) has been derived.”