Genuine multipartite entanglement in a one-dimensional Bose-Hubbard model with frustrated hopping

TL;DR

This study investigates how frustration affects genuine multipartite entanglement in a one-dimensional Bose-Hubbard model, revealing complex behaviors and emphasizing the need to distinguish between ordering and entanglement in quantum many-body systems.

Contribution

It provides a detailed analysis of multipartite entanglement in a frustrated Bose-Hubbard model, highlighting the nuanced relationship between frustration, quantum fluctuations, and entanglement.

Findings

Multipartite entanglement exhibits rich behavior across parameters.

Frustration does not always increase multipartite entanglement.

Strong quantum fluctuations lead to particle delocalization and low entanglement.

Abstract

Frustration and quantum entanglement are two exotic quantum properties in quantum many-body systems. However, despite several efforts, an exact relation between them remains elusive. In this work, we explore the relationship between frustration and quantum entanglement in a physical model describing strongly correlated ultracold bosonic atoms in optical lattices. In particular, we consider the one-dimensional Bose-Hubbard model comprising both nearest-neighbor ($t_{1}$) and frustrated next-nearest neighbor ($t_{2}$) hoppings and examine how the interplay of onsite interaction ($U$) and hoppings results in different quantum correlations dominating in the ground state of the system. We then analyze the behavior of quantum entanglement in the model. In particular, we compute genuine multipartite entanglement as quantified through the generalized geometric measure and make a comparative study with bipartite entanglement and other relevant order parameters. We observe that genuine multipartite entanglement has a very rich behavior throughout the considered parameter regime and frustration does not necessarily favor generating a high amount of it. Moreover, we show that in the region with strong quantum fluctuations, the particles remain highly delocalized in all momentum modes and share a very low amount of both bipartite and multipartite entanglement. Our work illustrates the necessity to give separate attention to dominating ordering behavior and quantum entanglement in the ground state of strongly correlated systems.