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Local convertibility and the quantum simulation of edge states in many-body systems
Citation
Franchini, F., Cui, J., Amico, L., Fan, H., Gu, M., Korepin, V., Kwek, L. C., & Vedral, V. (2014). Local convertibility and the quantum simulation of edge states in many-body systems. Physical Review X, 4(4), Article 041028. https://doi.org/10.1103/PhysRevX.4.041028
Author
Franchini, Fabio
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Cui, Jian
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Amico, Luigi
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Fan, Heng
•
Gu, Mile
•
Korepin, Vladimir
•
•
Vedral, Vlatko
Abstract
In some many-body systems, certain ground-state entanglement (Rényi) entropies increase even as the correlation length decreases. This entanglement nonmonotonicity is a potential indicator of nonclassicality. In this work, we demonstrate that such a phenomenon, known as lack of local convertibility, is due to the edge-state (de)construction occurring in the system. To this end, we employ the example of the Ising chain, displaying an order-disorder quantum phase transition. Employing both analytical and numerical methods, we compute entanglement entropies for various system bipartitions (A|B) and consider ground states with and without Majorana edge states. We find that the thermal ground states, enjoying the Hamiltonian symmetries, show lack of local convertibility if either A or B is smaller than, or of the order of, the correlation length. In contrast, the ordered (symmetry-breaking) ground state is always locally convertible. The edge-state behavior explains all these results and could disclose a paradigm to understand local convertibility in other quantum phases of matter. The connection we establish between convertibility and nonlocal, quantum correlations provides a clear criterion of which features a universal quantum simulator should possess to outperform a classical machine.
Date Issued
2014
Publisher
American Physical Society
Journal
Physical Review X
DOI
10.1103/PhysRevX.4.041028