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Extensive long-range entanglement at finite temperatures from a nonequilibrium bias
Physical Review B ( IF 3.2 ) Pub Date : 2024-07-19 , DOI: 10.1103/physrevb.110.035149 Shachar Fraenkel 1 , Moshe Goldstein 1
Physical Review B ( IF 3.2 ) Pub Date : 2024-07-19 , DOI: 10.1103/physrevb.110.035149 Shachar Fraenkel 1 , Moshe Goldstein 1
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Thermal equilibrium states of local quantum many-body systems are notorious for their spatially decaying correlations, which place severe restrictions on the types of many-body entanglement structures that may be observed at finite temperatures. These restrictions may, however, be defied when an out-of-equilibrium steady state is considered instead. In this paper, we study the entanglement properties of free fermions on a one-dimensional lattice that contains a generic charge- and energy-conserving noninteracting impurity, and that is connected at its edges to two reservoirs with different equilibrium energy distributions. These distributions may differ in either temperature, chemical potential, or both, thereby inducing an external bias. We analytically derive exact asymptotic expressions for several quantum information measures—the mutual information, its Rényi generalizations, and the fermionic negativity—that quantify the correlation and entanglement between two subsystems located on opposite sides of the impurity. We show that all these measures scale (to a leading order) linearly with the overlap between one subsystem and the mirror image of the other (upon reflection of the latter about the impurity), independently of the distance between the subsystems. While a simple proportionality relation between the negativity and Rényi versions of the mutual information is observed to hold at zero temperature, it breaks down at finite temperatures, suggesting that these quantities represent strong long-range correlations of different origins. Our results generalize previous findings that were limited to the case of a chemical-potential bias at zero temperature, rigorously demonstrating that the effect of long-range volume-law entanglement is robust at finite temperatures.
中文翻译：
非平衡偏压在有限温度下的广泛长程纠缠
局域量子多体系统的热平衡态因其空间衰减相关性而臭名昭著，这对在有限温度下可以观察到的多体纠缠结构的类型施加了严格的限制。然而，当考虑非平衡稳态时，这些限制可能会被打破。在本文中，我们研究了一维晶格上自由费米子的纠缠性质，该一维晶格包含通用的电荷和能量守恒的非相互作用杂质，并且在其边缘连接到具有不同平衡能量分布的两个储存库。这些分布可能在温度、化学势或两者上有所不同，从而引起外部偏差。我们通过分析推导了几种量子信息测度的精确渐近表达式——互信息、其 Rényi 泛化和费米子负性——量化了位于杂质两侧的两个子系统之间的相关性和纠缠。我们表明，所有这些测量都与一个子系统和另一个子系统的镜像之间的重叠（根据后者关于杂质的反射）线性缩放（到前导顺序），与子系统之间的距离无关。虽然观察到互信息的负性和 Rényi 版本之间的简单比例关系在零温度下保持不变，但它在有限温度下会崩溃，这表明这些量代表了不同来源的强长期相关性。我们的结果概括了先前仅限于零温度下化学势偏差情况的发现，严格证明了长程体积定律纠缠的效应在有限温度下是稳健的。
更新日期：2024-07-19
中文翻译：
非平衡偏压在有限温度下的广泛长程纠缠
局域量子多体系统的热平衡态因其空间衰减相关性而臭名昭著，这对在有限温度下可以观察到的多体纠缠结构的类型施加了严格的限制。然而，当考虑非平衡稳态时，这些限制可能会被打破。在本文中，我们研究了一维晶格上自由费米子的纠缠性质，该一维晶格包含通用的电荷和能量守恒的非相互作用杂质，并且在其边缘连接到具有不同平衡能量分布的两个储存库。这些分布可能在温度、化学势或两者上有所不同，从而引起外部偏差。我们通过分析推导了几种量子信息测度的精确渐近表达式——互信息、其 Rényi 泛化和费米子负性——量化了位于杂质两侧的两个子系统之间的相关性和纠缠。我们表明，所有这些测量都与一个子系统和另一个子系统的镜像之间的重叠（根据后者关于杂质的反射）线性缩放（到前导顺序），与子系统之间的距离无关。虽然观察到互信息的负性和 Rényi 版本之间的简单比例关系在零温度下保持不变，但它在有限温度下会崩溃，这表明这些量代表了不同来源的强长期相关性。我们的结果概括了先前仅限于零温度下化学势偏差情况的发现，严格证明了长程体积定律纠缠的效应在有限温度下是稳健的。
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