Entanglement signatures of quantum Hall phase transitions

Abstract

We study quantum phase transitions involving fractional quantum Hall states, using numerical calculations of entanglements and related quantities. We tune finite-size wavefunctions on spherical geometries, by varying the interaction potential away from the Coulomb interaction. We uncover signatures of quantum phase transitions contained in the scaling behavior of the entropy of entanglement between two parts of the sphere. In addition to the entanglement entropy, we show that signatures of quantum phase transitions also appear in other aspects of the reduced density matrix of one part of the sphere.

8 pages, 7 figures

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• Entanglement Entropy and Spectra of the One-dimensional Kugel-Khomskii Model
• Interaction-tuned compressible-to-incompressible phase transitions in the quantum Hall systems
• Entanglement Spectra of the quantum hard-square model: Holographic minimal models
• Entanglement Spectra of Heisenberg Ladders of higher Spin
• Scaling of entanglement in $2+1$-dimensional scale-invariant field theories
• Entanglement spectrum: Identification of the transition from vortex-liquid to vortex-lattice state in a weakly interacting rotating Bose-Einstein condensate
• Entanglement Spectrum and Entanglement Hamiltonian of a Chern insulator with open boundaries
• On integrable matrix product operators with bond dimension $D=4$
• Spin-singlet Gaffnian wave function for fractional quantum Hall systems