Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China.
Department of Physics, School of Science, Westlake University, 600 Dunyu Road, Hangzhou, 310030, Zhejiang Province, China.
Nat Commun. 2023 Apr 24;14(1):2360. doi: 10.1038/s41467-023-37756-7.
Based on the path integral formulation of the reduced density matrix, we develop a scheme to overcome the exponential growth of computational complexity in reliably extracting low-lying entanglement spectrum from quantum Monte Carlo simulations. We test the method on the Heisenberg spin ladder with long entangled boundary between two chains and the results support the Li and Haldane's conjecture on entanglement spectrum of topological phase. We then explain the conjecture via the wormhole effect in the path integral and show that it can be further generalized for systems beyond gapped topological phases. Our further simulation results on the bilayer antiferromagnetic Heisenberg model with 2D entangled boundary across the (2 + 1)D O(3) quantum phase transition clearly demonstrate the correctness of the wormhole picture. Finally, we state that since the wormhole effect amplifies the bulk energy gap by a factor of β, the relative strength of that with respect to the edge energy gap will determine the behavior of low-lying entanglement spectrum of the system.
基于约化密度矩阵的路径积分公式，我们提出了一种方案，以克服在从量子蒙特卡罗模拟中可靠地提取低能纠缠谱时计算复杂度呈指数增长的问题。我们在具有两条链之间长纠缠边界的海森堡梯型模型上测试了该方法，结果支持 Li 和 Haldane 关于拓扑相纠缠谱的猜想。然后，我们通过路径积分中的虫洞效应解释了该猜想，并表明它可以进一步推广到具有间隙拓扑相之外的系统。我们在具有二维纠缠边界的双层反铁磁海森堡模型上的进一步模拟结果，跨越（2+1）D O(3) 量子相变，清楚地证明了虫洞图像的正确性。最后，我们指出，由于虫洞效应将体能隙放大了β倍，因此它与边缘能隙的相对强度将决定系统低能纠缠谱的行为。
