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Phys Rev Lett. 2006 Oct 13;97(15):150404. Epub 2006 Oct 12.

General entanglement scaling laws from time evolution.

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1
Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW, United Kingdom and Institute for Mathematical Sciences, Imperial College London, Prince's Gardens, London SW7 2PE, United Kingdom.

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 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.

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