Entanglement distribution in fermion model with long-range interaction

Abstract

How two-party entanglement (TPE) is distributed in the many-body systems? This is a fundamental issue because the total TPE between one party with all the other parties, ${\mathcal{C}}^N$, is upper bounded by the Coffman, Kundu and Wootters (CKW) monogamy inequality, from which ${\mathcal{C}}^N\le \sqrt{N-1}$ can be proved by the geometric inequality. Here we explore the total entanglement ${\mathcal{C}}^{\infty }$ and the associated total tangle ${\tau }^{\infty }$ in a $p$-wave free fermion model with long-range interaction, showing that ${\mathcal{C}}^{\infty }\sim \mathcal{O}(1)$ and ${\tau }^{\infty }$ may become vanishing small with the increasing of long-range interaction. However, we always find ${\mathcal{C}}^{\infty }\sim 2\xi {\tau }^{\infty }$, where $\xi$ is the truncation length of entanglement, beyond which the TPE is quickly vanished, hence ${\tau }^{\infty }\sim 1/\xi$. This relation is a direct consequence of the exponential decay of the TPE induced by the long-range interaction. These results unify the results in the Lipkin-Meshkov-Glick (LMG) model and Dicke model and generalize the Koashi, Buzek and Imono bound to the quantum many-body models, with much broader applicability.

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Cited by in corpus (1)

• Long-range bipartite entanglement in XXZ spin chains with the exponential and power-law long-range interactions