Entanglement Entropy in Extended Quantum Systems

Abstract

After a brief introduction to the concept of entanglement in quantum systems, I apply these ideas to many-body systems and show that the von Neumann entropy is an effective way of characterising the entanglement between the degrees of freedom in different regions of space. Close to a quantum phase transition it has universal features which serve as a diagnostic of such phenomena. In the second part I consider the unitary time evolution of such systems following a `quantum quench' in which a parameter in the hamiltonian is suddenly changed, and argue that finite regions should effectively thermalise at late times, after interesting transient effects.

6 pages. Plenary talk delivered at Statphys 23, Genoa, July 2007

References in corpus (9)

• Entanglement Entropy and Quantum Field Theory
• Concentrating Partial Entanglement by Local Operations
• Geometric and Renormalized Entropy in Conformal Field Theory
• Time-dependence of correlation functions following a quantum quench
• Universality of Entropy Scaling in 1D Gap-less Models
• Entanglement entropy of random quantum critical points in one dimension
• Quench dynamics across quantum critical points
• Evolution of entanglement after a local quench
• On the entanglement entropy for a XY spin chain

Cited by in corpus (19)

• Entanglement entropy and conformal field theory
• Quantum trajectories and open many-body quantum systems
• Quantum Quench from a Thermal Initial State
• Entanglement in non-unitary quantum critical spin chains
• Inhomogeneous Quantum Quenches
• Thermodynamics and its Prediction and CALPHAD Modeling: Review, State of the Art, and Perspectives
• Entanglement Content of Quasi-Particle Excitations
• Excited state entanglement in homogeneous fermionic chains
• Entanglement, combinatorics and finite-size effects in spin-chains
• Counting statistics for non-interacting fermions in a $d$-dimensional potential
• Entanglement entropy and the complex plane of replicas
• Entanglement convertibility by sweeping through the quantum phases of the alternating bonds $XXZ$ chain
• Entanglement of several blocks in fermionic chains
• Parent Hamiltonian Reconstruction of Jastrow-Gutzwiller Wavefunctions
• Spin-models, dynamics and criticality with atoms in tilted optical superlattices
• Interacting quantum walk on a graph
• Localization and the interface between quantum mechanics, quantum field theory and quantum gravity II (The search of the interface between QFT and QG)
• Reduced density matrix and entanglement entropy of permutationally invariant quantum many-body systems
• Out of equilibrium mean field dynamics in the transverse field Ising model