Manifestations of topological band crossings in bulk entanglement spectrum: An analytical study for integer quantum Hall states

Abstract

We consider integer quantum Hall states and calculate bulk entanglement spectrum by formulating the correlation matrix in guiding center representation. Our analytical approach is based on the projection operator with redefining the inner product of states in Hilbert space to take care of the restriction imposed by the (rectangle-tiled) checkerboard partition. The resultant correlation matrix contains the coupling constants between states of different guiding centers parameterized by magnetic length and the period of partition. We find various band-crossings by tuning the flux $\Phi$ threading each chekerborad pixel and by changing filling factor $\nu$. When $\nu =1$ and $\Phi =2\pi$, or $\nu =2$ and $\Phi =\pi$, one Dirac band crossing is found. For $\nu =1$ and $\Phi =\pi$, the band crossings are in the form of nodal line, enclosing the Brillouin zone. As for $\nu =2$ and $\Phi =2\pi$, the doubled Dirac point, or the quadratic point, is seen. Besides, we infer that the quadratic point is protected by C${}_4$ symmetry of the checkerboard partition since it evolves into two separate Dirac points when the symmetry is lowered to C${}_2$. In addition, we also identify the emerging symmetries responsible for the symmetric bulk entanglement spectra, which are absent in the underlying quantum Hall states.

8 pages, 5 figures

References in corpus (11)

• Classification of topological insulators and superconductors in three spatial dimensions
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• First direct observation of Spin-textures in Topological Insulators : Spin-resolved ARPES as a probe of topological quantum spin Hall effect and Berry's phase
• Fluctuations and Entanglement spectrum in quantum Hall states
• Critical entanglement spectrum of one-dimensional symmetry protected topological phases
• Entanglement Chern number for an extensive partition of a topological ground state
• Tensor Network Implementation of Bulk Entanglement Spectrum
• Entanglement Spectrum of a Random Partition: Connection with the Localization Transition
• Disentangled topological numbers by a purification of entangled mixed states for non-interacting fermion systems
• Zero modes of the generalized fermion-vortex system in magnetic field
• Topologically distinct critical theories emerging from the bulk entanglement spectrum of integer quantum Hall states on a lattice

Cited by in corpus (3)

• Bulk Entanglement Spectrum in Gapped Spin Ladders
• Refined Characterization of Lattice Chern Insulators by Bulk Entanglement Spectrum
• Emergent infinite-randomness fixed points from the extensive random bipartitions of the spin-1 Affleck-Kennedy-Lieb-Tasaki topological state