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

We develop a nonequilibrium increment method in quantum Monte Carlo simulations to obtain the Renyi 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.

Automated summary

In this paper, we develop a nonequilibrium increment method in quantum Monte Carlo simulations to efficiently and accurately obtain the Renyi entanglement entropy of various quantum many-body systems. The method is demonstrated on several important quantum lattice models, and it successfully reveals the precise conformal field theory data and extracts the quantum dimension in topological order. The method establishes a controlled and practical computation paradigm for studying the universal properties in highly entangled quantum matter.