2006/03/31 by Jens Eisert, Tobias J. Osborne · 6 citations
Computer Science · Mathematics · Physics and Astronomy · #Entropy (arrow of time) #Geometry #Hamiltonian (control theory) #Law #Mathematics #Model Reduction and Neural Networks #Neural Networks and Reservoir Computing #Physics #Quantum #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Scaling #Statistical physics #Theoretical physics #cond-mat.stat-mech #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1103/physrevlett.97.150404
published as Phys. Rev. Lett. 97, 150404 (2006) · 4 pages, 1 figure (see also related work by S. Bravyi, M. Hastings, and F. Verstraete, quant-ph/0603121); replaced with final version
arxiv created 2006/10/12 · openalex publication_date 2006/10/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We establish a general scaling law for the entanglement of a large class of ground states and dynamically evolving states of quantum spin chains: we show that the geometric entropy of a distinguished block saturates, and hence follows an entanglement-boundary law. These results apply to any ground state of a gapped model resulting from dynamics generated by a local Hamiltonian, as well as, dually, to states that are generated via a sudden quench of an interaction as recently studied in the case of dynamics of quantum phase transitions. We achieve these results by exploiting ideas from quantum information theory and tools provided by Lieb-Robinson bounds. We also show that there exist noncritical fermionic systems and equivalent spin chains with rapidly decaying interactions violating this entanglement-boundary law. Implications for the classical simulatability are outlined.