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- W3081001850 abstract "We prove that all Renyi entanglement entropies of spin-chains described by generic (gapped), translational invariant matrix product states (MPS) are extensive for disconnected sub-systems: All Renyi entanglement entropy densities of the sub-system consisting of every k-th spin are non-zero in the thermodynamic limit if and only if the state does not converge to a product state in the thermodynamic limit. Furthermore, we provide explicit lower bounds to the entanglement entropy in terms of the expansion coefficient of the transfer operator of the MPS and spectral properties of its fixed point in canonical form. As side-result we obtain a lower bound for the expansion coefficient and singular value distribution of a primitve quantum channel in terms of its Kraus-rank and entropic properties of its fixed-point. For unital quantum channels this yields a very simple lower bound on the distribution of singular values and the expansion coefficient in terms of the Kraus-rank. Physically, our results are motivated by questions about equilibration in many-body localized systems, which we review." @default.
- W3081001850 created "2020-09-01" @default.
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- W3081001850 date "2020-08-26" @default.
- W3081001850 modified "2023-09-28" @default.
- W3081001850 title "Extensive Rényi entropies in matrix product states" @default.
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