Universal and non-universal contributions of entanglement under different bipartitions

TL;DR

This study quantitatively analyzes how different bipartitions affect entanglement entropy at quantum critical points, revealing surface contributions can alter scaling and providing a robust method to identify bulk criticality.

Contribution

It introduces a modified scaling form that accounts for both bulk and surface critical modes, establishing a quantitative link between surface criticality and entanglement scaling.

Findings

Surface criticality significantly influences entanglement entropy scaling.

Extra gapless edge modes can reverse the sign of the constant term in EE.

Derivative of EE reliably detects bulk critical points and exponents.

Abstract

Entanglement entropy (EE) is a fundamental probe of quantum phases and critical phenomena, which was thought to reflect only bulk universality for a long time. Very recently, people realized that the microscopic geometry of the entanglement cut can induce distinct entanglement-edge modes, whose coupling to bulk critical fluctuations may alter the scaling of the EE. However, this perception is very qualitative and lacks quantitative consideration. Here, we investigate this problem through high-precision quantum Monte Carlo simulations combined with the analysis of scaling theory to build a quantitative understanding. By considering three distinct bipartitions corresponding to three surface criticality types, we reveal a striking dependence of the constant term {\gamma} on the microscopic cut at the quantum critical point. Notably, cuts that generate extra gapless edge modes yield a sign reversal in {\gamma} compared to those producing gapped edges. We explain this behavior via a modified scaling form that incorporates contributions from both bulk and surface critical modes. Furthermore, we demonstrate that the derivative of EE robustly extracts the bulk critical point and exponent {\nu} regardless of the cut geometry, providing a reliable diagnostic of bulk universality in the presence of strong surface effects. Our work for the first time establishes a direct quantitative connection between surface criticality and entanglement scaling, challenging the conventional view that EE solely reflects bulk properties and offering a refined framework for interpreting entanglement in systems with boundary-sensitive criticality.