Entanglement detachment in fermionic systems

TL;DR

This paper introduces the concept of entanglement detachment in fermionic systems, showing how increasing certain couplings can effectively isolate a block within the ground state, reducing entanglement with the environment.

Contribution

It presents the novel concept of entanglement detachment and demonstrates it through examples in free fermionic systems, analyzing the entanglement spectrum and Hamiltonian.

Findings

Detachment occurs with increased couplings in specific fermionic models.

Detached blocks show decreased entanglement entropy and increased internal correlations.

External fields can influence the detachment in star-graph systems.

Abstract

This article introduces and discusses the concept of entanglement detachment. Under some circumstances, enlarging a few couplings of a Hamiltonian can effectively detach a (possibly disjoint) block within the ground state. This detachment is characterized by a sharp decrease in the entanglement entropy between block and environment, and leads to an increase of the internal correlations between the (possibly distant) sites of the block. We provide some examples of this detachment in free fermionic systems. The first example is an edge-dimerized chain, where the second and penultimate hoppings are increased. In that case, the two extreme sites constitute a block which disentangles from the rest of the chain. Further examples are given by (a) a superlattice which can be detached from a 1D chain, and (b) a star-graph, where the extreme sites can be detached or not depending on the presence of an external magnetic field, in analogy with the Aharonov-Bohm effect. We characterize these detached blocks by their reduced matrices, specially through their entanglement spectrum and entanglement Hamiltonian.