Extracting Universal Corner Entanglement Entropy during the Quantum Monte Carlo Simulation

TL;DR

This paper introduces a new quantum Monte Carlo method to accurately measure universal corner entanglement entropy contributions in (2+1)D quantum critical systems, improving detection of subleading logarithmic corrections.

Contribution

The authors develop a computationally efficient approach to isolate and measure the universal corner entanglement entropy in quantum Monte Carlo simulations, reducing noise and eliminating non-universal terms.

Findings

Accurate calculation of corner log-coefficients in bilayer Heisenberg models.

Method effectively isolates universal corner contributions from other entanglement terms.

Results support further theoretical exploration of universal properties in interacting conformal field theories.

Abstract

The subleading corner logarithmic corrections in entanglement entropy (EE) are crucial for revealing universal characteristics of the quantum critical points (QCPs), but they are challenging to detect. Motivated by recent developments in the stable computation of EE in (2+1)D quantum many-body systems, we have developed a new method for directly measuring the corner contribution in EE with less computational cost. The cornerstone of our approach is to measure the subtracted corner entanglement entropy (SCEE) defined as the difference between the EEs of subregions with the same boundary length for smooth and cornered boundaries during the sign-problem free quantum Monte Carlo simulation. Our improved method inherently eliminates not only the area law term of EE but also the subleading log-corrections arising from Goldstone modes, leaving the universal corner contribution as the leading term of SCEE with greatly improved data quality. Utilizing this advanced approach, we calculate the SCEE of the bilayer Heisenberg model on both square and honeycomb lattices across their (2+1)D O(3) QCPs with different opening angles on entanglement boundary, and obtain the accurate values of the corresponding universal corner log-coefficients. These findings will encourage further theoretical investigations to access controlled universal information for interacting CFTs at (2+1)D.