Entanglement spectroscopy of chiral edge modes in the Quantum Hall effect

Abstract

We investigate the entanglement entropy in the Integer Quantum Hall effect in the presence of an edge, performing an exact calculation directly from the microscopic two-dimensional wavefunction. The edge contribution is shown to coincide exactly with that of a chiral Dirac fermion, and this correspondence holds for an arbitrary collection of intervals. In particular for a single interval the celebrated conformal formula is recovered with left and right central charges $c+\bar{c}=1$. Using Monte-Carlo techniques we establish that this behavior persists for strongly interacting systems such as Laughlin liquids. This illustrates how entanglement entropy is not only capable of detecting the presence of massless degrees of freedom, but also of pinpointing their position in real space, as well as elucidating their nature.

18 pages, 8 figures

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Cited by in corpus (19)

• Cornering the universal shape of fluctuations
• Equipartition of Entanglement in Quantum Hall States
• Fractional Chiral Hinge Insulator
• Universal signatures of Dirac fermions in entanglement and charge fluctuations
• The boundary density profile of a Coulomb droplet. Freezing at the edge
• Ergodic Edge Modes in the 4D Quantum Hall Effect
• Exponential moments for disk counting statistics of random normal matrices in the critical regime
• Geometric entanglement in integer quantum Hall states
• Entanglement entropies of an interval for the massless scalar field in the presence of a boundary
• Multipartite entanglement in two-dimensional chiral topological liquids
• Model wavefunctions for interfaces between lattice Laughlin states
• Entanglement entropy for integer quantum Hall effect in two and higher dimensions
• The entanglement entropy of the quantum Hall edge and its geometric contribution
• Entanglement for Quantum Hall states and a Generalized Chern-Simons Form
• Geometric entanglement in integer quantum Hall states with boundaries
• Off-diagonal estimates of partial Bergman kernels on $S^1$-symmetric Kähler manifolds
• Symmetry Resolved Entanglement Entropy in a Non-Abelian Fractional Quantum Hall State
• Second Rényi entropy and annulus partition function for one-dimensional quantum critical systems with boundaries
• Rényi entropies for one-dimensional quantum systems with mixed boundary conditions