AI 中文总结
本研究利用扩展不确定原理的几何修正，解决了量子系统中零模导致的红外纠缠发散问题，使纠缠熵饱和为有限值。
AI 中文摘要
量子系统的纠缠熵通常同时表现出紫外和红外（IR）发散。在低频极限下，红外发散与零模的无界空间离域密切相关，这是耦合谐振子和无质量标量场共有的病态特征。本研究表明，通过引入扩展不确定原理（EUP）可自然解决这种无限增长问题，该原理对正则对易关系引入了大尺度几何修正。通过在EUP框架下精确求解谐振子，我们证实存在一种固有几何约束，其对位置方差施加严格上限、限制空间离域，并引入与背景里奇标量相关的固有局域化长度尺度。我们将这种正则化机制扩展到多体系统，通过计算一维谐振链和无质量标量场的纠缠熵与纠缠谱，发现EUP诱导的空间边界阻止了低能长波模式的积累，即使在严格无质量极限下也能保持纠缠谱离散且均匀带隙。这种非零模隙有效限制了真空的局域纠缠温度，最终使纠缠熵饱和到有限值，为量子场论中的零模红外发散问题提供了一种稳健的几何解决方案。
英文摘要
The entanglement entropy of quantum systems typically exhibits both ultraviolet and infrared (IR) divergences. In the low-frequency limit, the IR divergence is intimately tied to the unbounded spatial delocalization of zero-modes, a pathological feature common to both coupled harmonic oscillators and massless scalar fields. In this work, we demonstrate that this infinite growth is naturally resolved by invoking the Extended Uncertainty Principle (EUP), which introduces large-length-scale geometric corrections to the canonical commutation relations. By exactly solving the simple harmonic oscillator under the EUP framework, we establish the existence of an intrinsic geometric confinement that enforces a strict upper bound on the position variance, limits spatial delocalization, and introduces an intrinsic localization length scale related to the background Ricci scalar. We extend this regularizing mechanism to many-body systems by evaluating the entanglement entropy and entanglement spectrum of a one-dimensional harmonic chain and a massless scalar field. We show that the EUP-induced spatial bounds prevent the accumulation of low-lying long-wavelength modes, keeping the entanglement spectrum discrete and evenly gapped even in the strictly massless limit. This non-vanishing modular gap effectively caps the local entanglement temperature of the vacuum. Consequently, the entanglement entropy saturates to a finite value, providing a robust, geometric resolution to the zero-mode IR divergence problem in quantum field theory.
Comments53 pages, 11 figures. Comments are welcome
