منابع مشابه
When Is an Area Law Not an Area Law?
Entanglement entropy is typically proportional to area, but sometimes it acquires an additional logarithmic pre-factor. We offer some intuitive explanations for these facts.
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We give a new proof for the area law for general 1D gapped systems, which exponentially improves Hastings’ famous result [1]. Specifically, we show that for a chain of d-dimensional spins, governed by a 1D local Hamiltonian with a spectral gap > 0, the entanglement entropy of the ground state with respect to any cut in the chain is upper bounded by O( log 3 d ). Our approach uses the framework ...
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We present a new proof for the 1D area law for frustration-free systems with a constant gap, which exponentially improves the entropy bound in Hastings 1D area law and which is tight to within a polynomial factor. For particles of dimension d, spectral gap > 0, and interaction strength of, at most, J , our entropy bound is S1D ≤ O(1) · X logX, where X def = (J log d)/ . Our proof is completely ...
متن کاملAn Area Law for One Dimensional Quantum Systems
We prove an area law for the entanglement entropy in gapped one dimensional quantum systems. The bound on the entropy grows surprisingly rapidly with the correlation length; we discuss this in terms of properties of quantum expanders and present a conjecture on completely positive maps which may provide an alternate way of arriving at an area law. We also show that, for gapped, local systems, t...
متن کاملar X iv : 1 51 1 . 02 99 6 v 1 [ he p - th ] 1 0 N ov 2 01 5 When is an area law not an area law ?
Entanglement entropy is typically proportional to area, but sometimes it acquires an additional logarithmic pre-factor. We offer some intuitive explanations for these facts.
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ژورنال
عنوان ژورنال: Entropy
سال: 2016
ISSN: 1099-4300
DOI: 10.3390/e18070240