Local Convertibility and the Quantum Simulation of Edge States in Many-Body Systems
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.
- Publication:
-
Physical Review X
- Pub Date:
- October 2014
- DOI:
- 10.1103/PhysRevX.4.041028
- arXiv:
- arXiv:1306.6685
- Bibcode:
- 2014PhRvX...4d1028F
- Keywords:
-
- 03.67.Mn;
- 03.67.Lx;
- 75.10.Pq;
- 03.67.Ac;
- Entanglement production characterization and manipulation;
- Quantum computation;
- Spin chain models;
- Quantum algorithms protocols and simulations;
- Condensed Matter - Statistical Mechanics;
- Condensed Matter - Strongly Correlated Electrons;
- High Energy Physics - Theory;
- Quantum Physics
- E-Print:
- Accepted by Physical Review X. 5 pages (+ 2 pages of Methods &