Area-law entanglement from quantum geometry

TL;DR

This paper investigates how quantum geometry influences entanglement entropy in fermionic systems, revealing a geometric contribution to the area-law violation and proposing experimental detection methods.

Contribution

It introduces a quantitative analysis of quantum geometric effects on entanglement entropy and provides numerical results for various models, connecting geometry with entanglement scaling.

Findings

Quantum geometry contributes to entanglement entropy scaling.

Numerical results for SSH, Dirac, and Chern models support the theory.

Proposed experimental probe via particle number fluctuations.

Abstract

Quantum geometry, which encompasses both Berry curvature and the quantum metric, plays a key role in multi-band interacting electron systems. We study the entanglement entropy of a region of linear size $\ell$ in fermion systems with nontrivial quantum geometry, i.e. whose Bloch states have nontrivial $k$ dependence. We show that the entanglement entropy scales as $S = \alpha \ell^{d-1} \ln\ell + \beta \ell^{d-1} + \cdots$ where the first term is the well-known area-law violating term for fermions and $\beta$ contains the leading contribution from quantum geometry. We compute this for the case of uniform quantum geometry and cubic domains and provide numerical results for the Su-Schrieffer-Heeger model, 2D massive Dirac cone, and 2D Chern bands. An experimental probe of the quantum geometric entanglement entropy is proposed using particle number fluctuations. We offer an intuitive account of the area-law entanglement related to the spread of maximally localized Wannier functions.