Engineering large end-to-end correlations in finite fermionic chains

TL;DR

This paper investigates how to engineer finite fermionic chains with large end-to-end correlations by deforming the SSH model, revealing optimal configurations and the exponential decay of maximum correlations with system size.

Contribution

It introduces a machine-learning approach to optimize correlations in fermionic chains and identifies near-optimal edge-dimerized configurations for large correlations.

Findings

Edge-dimerized chains are near-optimal configurations.

Maximum correlation decays exponentially with chain length.

Bulk entanglement patterns remain similar to the clean case.

Abstract

We explore deformations of finite chains of independent fermions which give rise to large correlations between their extremes. After a detailed study of the Su-Schrieffer-Heeger (SSH) model, the trade-off curve between end-to-end correlations and the energy gap of the chains is obtained using machine-learning techniques, paying special attention to the scaling behavior with the chain length. We find that edge-dimerized chains, where the second and penultimate hoppings are reinforced, are very often close to the optimal configurations. Our results allow us to conjecture that, given a fixed gap, the maximal attainable correlation falls exponentially with the system size. Study of the entanglement entropy and contour of the optimal configurations suggest that the bulk entanglement pattern is minimally modified from the clean case.