Abstract

We investigate how entangled states can be created by considering collections of point-particles arranged at different spatial configurations, i.e., Fock states with spatial constraints. This type of states can be realized in Hubbard chains of spinless hard-core bosons, at different fillings, which have gapped energy spectrum with a highly degenerate ground state. We calculate the bipartite entanglement entropy for superpositions of such Fock states and show that their entanglement can be controlled via the spatial freedom of the particles, determined by the system filling. In addition we study the effect of confinement/boundary conditions on the Fock states and show that edge modes appear at the ends of the system, when open boundary conditions are considered. Our result is an example of entangled many-body states in 1D systems of strongly interacting particles, without requiring the spin, long-range microscopic interactions or external fields. Instead, the entanglement can be tuned by the empty space in the system, which determines the spatial freedom of the interacting particles.

Graphical abstract

中文翻译：

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具有空间约束的多体Fock态叠加的纠缠和边缘效应

摘要

我们研究如何通过考虑以不同空间配置（即具有空间约束的Fock状态）布置的点粒子的集合来创建纠缠状态。这种类型的状态可以在不同填充物的无旋转硬核玻色子的哈伯德链中实现，它们的能谱具有高度退化的基态。我们为这种Fock态的叠加计算了二分纠缠熵，并表明可以通过系统填充确定粒子的空间自由度来控制它们的纠缠。此外，我们研究了约束/边界条件对Fock状态的影响，并表明当考虑开放边界条件时，边缘模式出现在系统的末端。我们的结果是一例强相互作用粒子在一维系统中纠缠多体状态的示例，而无需旋转，远距离微观相互作用或外部场。取而代之的是，纠缠可以通过系统中的空白空间进行调整，这确定了相互作用粒子的空间自由度。

图形概要