Entanglement corner dependence in two-dimensional systems: A tensor network perspective

TL;DR

This paper demonstrates that entanglement corner dependence in continuous quantum field theories can be understood through the geometric structure of tensor networks, specifically iPEPS, on discrete lattices, highlighting the importance of averaging over lattice orientations.

Contribution

It reveals how corner-dependent entanglement contributions naturally arise in tensor network representations and connects continuum predictions with discrete lattice structures, including gauge-invariant systems.

Findings

Corner dependence emerges from bond dimension counting in iPEPS.

Averaging over lattice orientations is essential for correspondence.

Additional corner terms appear in gauge-invariant systems.

Abstract

In continuous quantum field theories, the entanglement entropy of a subsystem with sharp corners on its boundary exhibits a universal corner-dependent contribution. We study this contribution through the lens of lattice discretization, and demonstrate that this corner dependence emerges naturally from the geometric structure of infinite projected entangled pair states (iPEPS) on discrete lattices. Using a rigorous counting argument, we show that the bond dimension of an iPEPS representation exhibits a corner-dependent term that matches the predicted term in gapped continuous systems. Crucially, we find that this correspondence only emerges when averaging over all possible lattice orientations and origin positions, revealing a fundamental requirement for properly discretizing continuous systems. Our results provide a geometric understanding of entanglement corner laws and establish a direct connection between continuum field theory predictions and the structure of discrete tensor network representations. We extend our analysis to gauge-invariant systems, where lattice corners crossed by the bipartition boundary contribute an additional corner-dependent term. These findings offer new insights into the relationship between entanglement in continuous and discrete quantum systems.