General entanglement scaling laws from time evolution

Abstract

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 making use of the powerful tools provided by Lieb-Robinson bounds. We also show that there exist noncritical fermionic systems and equivalent spin chains with rapidly decaying interactions whose geometric entropy scales logarithmically with block length. Implications for the classical simulatability are outlined.

4 pages, 1 figure (see also related work by S. Bravyi, M. Hastings, and F. Verstraete, quant-ph/0603121); replaced with final version

References in corpus (10)

• Multi-party entanglement in graph states
• Matrix product states represent ground states faithfully
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Criticality, the area law, and the computational power of PEPS
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Ground state entanglement and geometric entropy in the Kitaev's model
• The Propagation of Quantum Information Through a Spin System
• Improved transfer of quantum information using a local memory

Cited by in corpus (20)

• Exact relaxation in a class of non-equilibrium quantum lattice systems
• Entanglement and correlation functions following a local quench: a conformal field theory approach
• Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
• Quantum Noise as an Entanglement Meter
• Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model
• Propagation of Correlations in Quantum Lattice Systems
• Evolution of entanglement after a local quench
• Autocorrelations and Thermal Fragility of Anyonic Loops in Topologically Quantum Ordered Systems
• Exploring local quantum many-body relaxation by atoms in optical superlattices
• Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems
• Adiabatic Preparation of Topological Order
• Fundamentals of universality in one-way quantum computation
• Entanglement in a periodic quench
• Lieb-Robinson bounds and the speed of light from topological order
• Observations Outside the Light-Cone: Algorithms for Non-Equilibrium and Thermal States
• Renormalization algorithm with graph enhancement
• A variational method based on weighted graph states
• Thermalization through unitary evolution of pure states
• On Spectral Gap,U(1) Symmetry and Split Property in Quantum Spin Chains
• Entanglement and ground states of gapped Hamiltonians