Measuring R\'enyi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations

TL;DR

This paper introduces a highly efficient quantum Monte Carlo method to accurately measure R'enyi entanglement entropy in complex quantum many-body systems, enabling detailed analysis of universal properties in highly entangled states.

Contribution

The authors develop a nonequilibrium increment method that significantly improves the efficiency and precision of R'enyi entanglement entropy measurements in quantum Monte Carlo simulations.

Findings

Successfully applied to various (2+1)d quantum lattice models

Revealed conformal field theory data from logarithmic corrections

Extracted quantum dimensions in topological orders

Abstract

We develop a nonequilibrium increment method in quantum Monte Carlo simulations to obtain the R\'enyi 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.