Probing Critical Surfaces in Momentum Space Using Real-Space Entanglement Entropy: Bose versus Fermi

TL;DR

This paper introduces a method to distinguish Fermi and Bose surfaces in momentum space by analyzing the leading logarithmic terms in real-space entanglement entropy, revealing fundamental differences and providing a new probe for critical surfaces.

Contribution

The authors demonstrate that the shape of critical surfaces can be inferred from entanglement entropy and reveal a fundamental factor of two difference between Bose and Fermi surfaces' entanglement signatures.

Findings

Logarithmic violation of entanglement entropy area law for critical surfaces.

Shape of critical surfaces can be determined from entanglement entropy.

Fermi and Bose surfaces differ by a factor of two in their logarithmic entanglement terms.

Abstract

A co-dimension one critical surface in the momentum space can be either a familiar Fermi surface, which separates occupied states from empty ones in the non-interacting fermion case, or a novel Bose surface, where gapless bosonic excitations are anchored. Their presence gives rise to logarithmic violation of entanglement entropy area law. When they are convex, we show that the shape of these critical surfaces can be determined by inspecting the leading logarithmic term of real space entanglement entropy. The fundamental difference between a Fermi surface and a Bose surface is revealed by the fact that the logarithmic terms in entanglement entropies differ by a factor of two: $S^{Bose}_{log} = 2 S^{Fermi}_{log}$, even when they have identical geometry. Our method has remarkable similarity with determining Fermi surface shape using quantum oscillation. We also discuss possible probes of concave critical surfaces in momentum space.