Local Convertibility and the Quantum Simulation of Edge States in Many-Body Systems

• Main Authors: Franchini, Fabio (Contributor), Cui, Jian (Author), Amico, Luigi (Author), Fan, Heng (Author), Gu, Mile (Author), Korepin, Vladimir (Author), Kwek, Leong Chuan (Author), Vedral, Vlatko (Author)
• Other Authors: Massachusetts Institute of Technology. Department of Physics (Contributor)
• Format: Article
• Language: English
• Published: American Physical Society, 2014-11-17T17:00:11Z.
• Subjects: Article
• Online Access: Get fulltext

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.
Seventh Framework Programme (European Commission) (Marie Curie International Outgoing Fellowship Grant PIOF-PHY-276093)