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

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: $S_{log}^{Bose}=2S_{log}^{Fermi}$, 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.

4.5 pages; 5 Figures; Revised version published on PRB Rapid Communication

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Cited by in corpus (9)

• Quantum entanglement in condensed matter systems
• Topological Multipartite Entanglement in a Fermi Liquid
• The negativity contour: a quasi-local measure of entanglement for mixed states
• Metallic state in bosonic systems with continuously degenerate minima
• Capacity of entanglement and distribution of density matrix eigenvalues in gapless systems
• Entanglement entropy of composite Fermi liquid states on the lattice: In support of the Widom formula
• Fractionalized Excitations Revealed by Entanglement Entropy
• Nodal Line Entanglement Entropy: Generalized Widom Formula from Entanglement Hamiltonians
• Entanglement entropies and fermion signs of critical metals