Wang Ting-Tung, Song Menghan, Lyu Liuke, Witczak-Krempa William, Meng Zi Yang
Department of Physics and HK Institute of Quantum Science & Technology, The University of Hong Kong, Hong Kong, Hong Kong.
Département de Physique, Université de Montréal, Montréal, QC, Canada.
Nat Commun. 2025 Jan 2;16(1):96. doi: 10.1038/s41467-024-55354-z.
Quantum entanglement uncovers the essential principles of quantum matter, yet determining its structure in realistic many-body systems poses significant challenges. Here, we employ a protocol, dubbed entanglement microscopy, to reveal the multipartite entanglement encoded in the full reduced density matrix of the microscopic subregion in spin and fermionic many-body systems. We exemplify our method by studying the phase diagram near quantum critical points (QCP) in 2 spatial dimensions: the transverse field Ising model and a Gross-Neveu-Yukawa transition of Dirac fermions. Our main results are: i) the Ising QCP exhibits short-range entanglement with a finite sudden death of the LN both in space and temperature; ii) the Gross-Neveu QCP has a power-law decaying fermionic LN consistent with conformal field theory (CFT) exponents; iii) going beyond bipartite entanglement, we find no detectable 3-party entanglement with our two witnesses in a large parameter window near the Ising QCP in 2d, in contrast to 1d. We further establish the singular scaling of general multipartite entanglement measures at criticality and present an explicit analysis in the tripartite case.
量子纠缠揭示了量子物质的基本原理，然而，在实际的多体系统中确定其结构面临着重大挑战。在这里，我们采用一种称为纠缠显微镜的方案，来揭示自旋和费米子多体系统中微观子区域的完全约化密度矩阵中编码的多体纠缠。我们通过研究二维空间中量子临界点（QCP）附近的相图来举例说明我们的方法：横向场伊辛模型和狄拉克费米子的格罗斯 - 内夫 - 汤川相变。我们的主要结果是：i）伊辛QCP在空间和温度上都表现出短程纠缠，且纠缠负性存在有限的突然死亡；ii）格罗斯 - 内夫QCP具有与共形场论（CFT）指数一致的幂律衰减费米子纠缠负性；iii）超越两体纠缠，我们发现在二维伊辛QCP附近的一个大参数窗口中，与一维情况相反，我们的两个见证者没有检测到三方纠缠。我们进一步确定了临界时一般多体纠缠度量的奇异标度，并在三方情况下进行了明确分析。
