Local convertibility and the quantum simulation of edge states in many-body systems

TL;DR

This paper investigates how edge states influence entanglement properties in many-body quantum systems, revealing that edge state dynamics cause non-local convertibility, which impacts quantum simulation capabilities.

Contribution

It demonstrates that edge state (de)construction explains non-local convertibility in many-body systems, linking entanglement behavior to quantum phase transitions and simulation potential.

Findings

Thermal ground states show non-local convertibility when subsystem size is small.

Ordered ground states are always locally convertible.

Edge states behavior explains entanglement non-monotonicity and convertibility.

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.