Entanglement entropy in fermionic Laughlin states

Abstract

We present analytic and numerical calculations on the bipartite entanglement entropy in fractional quantum Hall states of the fermionic Laughlin sequence. The partitioning of the system is done both by dividing Landau level orbitals and by grouping the fermions themselves. For the case of orbital partitioning, our results can be related to spatial partitioning, enabling us to extract a topological quantity (the `total quantum dimension') characterizing the Laughlin states. For particle partitioning we prove a very close upper bound for the entanglement entropy of a subset of the particles with the rest, and provide an interpretation in terms of exclusion statistics.

4+ pages, 3 figures. Minor changes in v2

References in corpus (5)

• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Entanglement scaling in critical two-dimensional fermionic and bosonic systems
• Entropy and Exact Matrix Product Representation of the Laughlin Wave Function

Cited by in corpus (13)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement and topological entropy of the toric code at finite temperature
• Bipartite entanglement entropy in fractional quantum Hall states
• Entanglement entropy and multifractality at localization transitions
• Entanglement signatures of quantum Hall phase transitions
• Topological phases and topological entropy of two-dimensional systems with finite correlation length
• Entropy and Exact Matrix Product Representation of the Laughlin Wave Function
• Particle partitioning entanglement in itinerant many-particle systems
• Subarea law of entanglement in nodal fermionic systems
• Skein Theory and Topological Quantum Registers: Braiding Matrices and Topological Entanglement Entropy of Non-Abelian Quantum Hall States
• Entanglement and level crossings in frustrated ferromagnetic rings
• Topological Entropy of Quantum Hall States in Rotating Bose Gases
• Entanglement of Valence-Bond-Solid on an Arbitrary Graph