Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations

• Published in: npj quantum materials Vol. 7; no. 1; pp. 1 - 9
• Main Authors: Zhao, Jiarui, Chen, Bin-Bin, Wang, Yan-Cheng, Yan, Zheng, Cheng, Meng, Meng, Zi Yang
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 29.06.2022; Nature Publishing Group; Nature Portfolio
• Subjects: 639/766/119/2792; 639/766/119/2795; Algorithms; Antiferromagnetism; Broken symmetry; Condensed Matter Physics; Critical point; Efficiency; Entropy; Field theory; Phase transitions; Physics; Physics and Astronomy; Quantum Physics; Simulation; Spin liquid; Structural Materials; Surfaces and Interfaces; Symmetry; Thin Films; Topology
• ISSN: 2397-4648; 2397-4648
• DOI: 10.1038/s41535-022-00476-0

We develop a nonequilibrium increment method in quantum Monte Carlo simulations to obtain the Rényi entanglement entropy of various quantum many-body systems with high efficiency and precision. To demonstrate its power, we show the results on a few important yet difficult (2 + 1) d quantum lattice models, ranging from the Heisenberg quantum antiferromagnet with spontaneous symmetry breaking, the quantum critical point with O(3) conformal field theory (CFT) to the toric code Z 2 topological ordered state and the Kagome Z 2 quantum spin liquid model with frustration and multi-spin interactions. In all these cases, our method either reveals the precise CFT data from the logarithmic correction or extracts the quantum dimension in topological order, from the dominant area law in finite-size scaling, with very large system sizes, controlled errorbars, and minimal computational costs. Our method, therefore, establishes a controlled and practical computation paradigm to obtain the difficult yet important universal properties in highly entangled quantum matter.