Abstract
In some many-body systems, certain ground state entanglement (Renyi) entropies increase even as the correlation length decreases. This entanglement non-monotonicity is a potential indicator of non-classicality. In this work we demonstrate that such a phenomenon, known as non-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 transitions. 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 non-local convertibility if either A or B are smaller than, or of the order of, the correlation length. In contrast, the ordered (symmetry breaking) ground state is always locally convertible. The edge states 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 non-local, quantum correlations provides a clear criterion of which features a universal quantum simulator should possess to outperform a classical machine.
Highlights
In 1982, Richard Feynman conjectured that a quantum machine is necessary to predict the outcome of a general quantum evolution and pioneered the notion of a universal quantum simulator: a device capable of processing quantum information that potentially supersedes any classical computer in simulating quantum systems
How can we determine if a many-body system can operate as an efficient quantum simulator? To what extent is coherent manipulation the defining property of a quantum algorithm? We address such a question quantitatively, using the local convertibility of the quantum system hosting the simulation, and we demonstrate that the (Majorana) edge states establish genuinely quantum long-range correlations that may provide an additional resource for a given computational protocol
In phases where differential local convertibility holds, the response of the ground state to an external perturbation can be rendered by local means, and such phases offer more restricted computational capability under adiabatic perturbation
Summary
In 1982, Richard Feynman conjectured that a quantum machine is necessary to predict the outcome of a general quantum evolution and pioneered the notion of a universal quantum simulator: a device capable of processing quantum information that potentially supersedes any classical computer in simulating quantum systems. These correlations are the manifestation of the edge states created at the boundaries between the subregions These considerations are reflected by the nontrivial behavior of the entanglement entropy: For some (low) α’s, the Rényi entropies are sensitive to short-range entanglement and increase when a quantum phase transition (QPT) is approached, but for other (large) α’s, the entropies do the opposite. This finding implies that the entanglement between edge states can decrease, even as the correlation length increases
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