论文标题

费米子高斯状态与截断方法之间的痕量距离

Trace distance between fermionic Gaussian states from a truncation method

论文作者

Zhang, Jiaju, Rajabpour, M. A.

论文摘要

在本文中,我们提出了一种新型的截断方法,用于确定费米管系统中两个高斯状态之间的痕量距离。对于以其相关矩阵为特征的两个费米子高斯状态,我们考虑了von Neumann的熵和相关矩阵之间的差异,并截断了相关矩阵以促进痕量距离计算。我们的方法在两种不同的情况下表现出显着的功效。在第一种情况下,各州具有小的von neumann熵,表明有限或对数的熵,而其相关矩阵显示出几乎交互的行为,其特征是相关矩阵交通量相对于系统大小的相关矩阵换入器的跟踪标准的有限或逐渐非线性。第二种情况包括两个状态几乎正交的情况,最大的规范值差异接近2。为了评估我们方法的性能,我们将其应用于各种引人注目的示例。值得注意的是,我们成功地计算了ISING和XX旋转链的低谎言特征态之间的子系统痕量距离,即使对于显着较大的子系统尺寸也是如此。这与现有文献形成鲜明对比,在该文献中,子系统痕量距离仅限于大约十个站点的子系统。通过我们的截断方法,我们将分析扩展到包含数百个站点的子系统,从而扩大了该领域的研究范围。

In this paper, we propose a novel truncation method for determining the trace distance between two Gaussian states in fermionic systems. For two fermionic Gaussian states, characterized by their correlation matrices, we consider the von Neumann entropies and dissimilarities between their correlation matrices and truncate the correlation matrices to facilitate trace distance calculations. Our method exhibits notable efficacy in two distinct scenarios. In the first scenario, the states have small von Neumann entropies, indicating finite or logarithmic-law entropy, while their correlation matrices display near-commuting behavior, characterized by a finite or gradual nonlinear increase in the trace norm of the correlation matrix commutator relative to the system size. The second scenario encompasses situations where the two states are nearly orthogonal, with a maximal canonical value difference approaching 2. To evaluate the performance of our method, we apply it to various compelling examples. Notably, we successfully compute the subsystem trace distances between low lying eigenstates of Ising and XX spin chains, even for significantly large subsystem sizes. This is in stark contrast to existing literature, where subsystem trace distances are limited to subsystems of approximately ten sites. With our truncation method, we extend the analysis to subsystems comprising several hundred sites, thus expanding the scope of research in this field.

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