nLab
entanglement entropy

Contents

Context

Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

Measure and probability theory

Contents

Idea

entropy induced by entanglement in quantum physics, really a synonym for subsystem entropy

If ρ\rho is a quantum state (density matrix) of some quantum systems and AA is a subsystem with complementary subsystem A¯\bar A, the its entanglement entropy is

S A=Tr A(ρ Alnρ A) S_A \;=\; - Tr_{A}\big( \rho_A \ln \rho_A \big)

for

ρ ATr A¯(ρ). \rho_A \;\coloneqq\; Tr_{\bar A}(\rho) \,.

quantum probability theoryobservables and states

References

General

  • Matthew Headrick, Lectures on entanglement entropy in field theory and holography (arXiv:1907.08126)

In AQFT:

See also

Topological entanglement entropy

Identification of a non-vanishing contribution to the (entanglement-)entropy at absolute zero, due to topological order/topological phase (“topological entropy”):

Review:

Experimental observation:

  • A. Hamma, W. Zhang, S. Haas, and D. A. Lidar, Entanglement, fidelity, and topological entropy in a quantum phase transition to topological order, Phys. Rev. B 77, 155111 (2008) (doi:10.1103/PhysRevB.77.155111, arXiv:0705.0026)

  • Hong-Chen Jiang, Zhenghan Wang, Leon Balents, Identifying Topological Order by Entanglement Entropy, Nature Physics 8, 902-905 (2012) (arXiv:1205.4289)

In terms of Renyi entropy (it’s independent of the Renyi entropy parameter):

  • Ulrich Schollwöck, (Almost) 25 Years of DMRG - What Is It About? (pdf)

Discussion in the dimer model:

  • Shunsuke Furukawa, Gregoire Misguich, Topological Entanglement Entropy in the Quantum Dimer Model on the Triangular Lattice, Phys. Rev. B 75, 214407 (2007) (arXiv:cond-mat/0612227)

Discussion via holographic entanglement entropy:

  • Ari Pakman, Andrei Parnachev, Topological Entanglement Entropy and Holography, JHEP 0807: 097 (2008) (arXiv:0805.1891)

  • Andrei Parnachev, Napat Poovuttikul, Topological Entanglement Entropy, Ground State Degeneracy and Holography, Journal of High Energy Physics volume 2015, Article number: 92 (2015) (arXiv:1504.08244)

See also:

  • Tatsuma Nishioka, Tadashi Takayanagi, Yusuke Taki, Topological pseudo entropy (arXiv:2107.01797)

Last revised on July 6, 2021 at 04:18:09. See the history of this page for a list of all contributions to it.