Precise computation of universal corner entanglement entropy at 2+1 dimension: From Ising to Gaussian quantum critical points

TL;DR

This paper develops a new quantum Monte Carlo algorithm to accurately compute the universal corner entanglement entropy in (2+1)d quantum critical systems, confirming theoretical predictions at Ising and Gaussian critical points.

Contribution

The authors introduce a bubble basis projector QMC method for precise entanglement entropy calculations at quantum critical points in (2+1)d systems, bridging theory and numerical results.

Findings

Quantitative agreement with theoretical corner entropy at Gaussian tricritical point.

Consistent results for R'enyi entanglement entropy at Ising and first-order transitions.

Establishment of the connection between solvable limits and strongly correlated regimes.

Abstract

Computing the subleading logarithmic term in the entanglement entropy (EE) of (2+1)d quantum many-body systems remains a significant challenge, despite its central role in revealing universal information about quantum states and quantum critical points (QCPs). Building on recent algorithmic advances that enable the stable calculation of EE as an exponential observable~\cite{zhouIncremental2024,zhangIntegral2024,liaoExtracting2024}, we develop a {\it bubble basis} projector quantum Monte Carlo (QMC) algorithm to precisely and efficiently compute the universal corner of EE at QCPs in a (2+1)d square-lattice transverse-field Ising model augmented with a four-body interaction. Turning on this interaction allows us to trace an Ising critical line, reaching the tricritical point, and then a line of first-order phase transition. In (2+1)d, the tricritical point is described by the Gaussian theory, where a theoretical calculation of the corner logarithmic term in the 2nd R\'enyi entropy term is available~\cite{UniversalCasini2007}. Our QMC results are in quantitative agreement with this theoretical value, providing a highly nontrivial benchmark of the algorithm. Furthermore, we also study the R\'enyi EE at the Ising critical line and on the first-order transition line, obtaining results consistent with theoretical expectations. These findings establish the long-sought connection between the universal values of an exactly solvable limit and those of a strongly correlated regime at (2+1)d.