论文标题
量子关键时纠缠差距的闭合：量子球模型的情况
Closure of the entanglement gap at quantum criticality: The case of the Quantum Spherical Model
论文作者
论文摘要
纠缠光谱的研究是检测或阐明量子多体系统中普遍行为的强大工具。我们研究了在二维量子临界点处的纠缠（或schmidt）GAP $Δξ$的缩放（或Schmidt）GAP $Δξ$。我们专注于范式量子球形模型，该模型表现出二阶过渡，并且可以映射到具有附加外部约束的游离玻色子上。我们在分析上表明，施密特差距在临界点消失，尽管只是对数。对于圆环上的系统和半个系统的两部分，纠缠差距消失为$π^2/\ ln（l）$，而$ l $则是线性系统大小。纠缠差距在顺磁性阶段非零，并且在有序阶段表现出更快的衰变。重新缩放的差距$Δξ\ ln（l）$在过渡时显示了不同系统大小的交叉，尽管对数校正阻止了有限尺寸缩放的精确验证。有趣的是，跨相图的纠缠差距的变化反映在自旋旋转相关器的零模式特征向量中。在过渡时，量子波动产生了特征向量的非平凡结构，而在有序相中，它是平坦的。我们还表明，临界时的纠缠差距消失可以是定性的，但不能通过忽略零模式特征向量的结构而定量捕获。
The study of entanglement spectra is a powerful tool to detect or elucidate universal behaviour in quantum many-body systems. We investigate the scaling of the entanglement (or Schmidt) gap $δξ$, i.e., the lowest laying gap of the entanglement spectrum, at a two-dimensional quantum critical point. We focus on the paradigmatic quantum spherical model, which exhibits a second-order transition, and is mappable to free bosons with an additional external constraint. We analytically show that the Schmidt gap vanishes at the critical point, although only logarithmically. For a system on a torus and the half-system bipartition, the entanglement gap vanishes as $π^2/\ln(L)$, with $L$ the linear system size. The entanglement gap is nonzero in the paramagnetic phase and exhibits a faster decay in the ordered phase. The rescaled gap $δξ\ln(L)$ exhibits a crossing for different system sizes at the transition, although logarithmic corrections prevent a precise verification of the finite-size scaling. Interestingly, the change of the entanglement gap across the phase diagram is reflected in the zero-mode eigenvector of the spin-spin correlator. At the transition quantum fluctuations give rise to a non-trivial structure of the eigenvector, whereas in the ordered phase it is flat. We also show that the vanishing of the entanglement gap at criticality can be qualitatively but not quantitatively captured by neglecting the structure of the zero-mode eigenvector.
