Topologically distinct critical theories emerging from the bulk entanglement spectrum of integer quantum Hall states on a lattice

Abstract

The critical theories for the topological phase transitions of integer quantum Hall states to a trivial insulating state with the same symmetry can be obtained by calculating the ground state entanglement spectrum under a symmetric checkerboard bipartition. In contrast to the gapless edge excitations under the left-right bipartition, a quantum network with bulk gapless excitations naturally emerges at the Brillouin zone center without fine tuning. On a large finite lattice, the resulting critical theory for the $\nu =1$ state is the (2+1) dimensional relativistic quantum field theory characterized by a \textit{single} Dirac cone spectrum and a pair of \textit{fractionalized} zero-energy states, while for the $\nu =2$ state the critical theory exhibits a parabolic spectrum and no sign of fractionalization in the zero-energy states. A triangular correspondence is established among the bulk topological theory, gapless edge theory, and the critical theory via the ground state entanglement spectrum.

arXiv comment5 pages, 4 figures, published version

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• Decoding quantum criticalities from fermionic/parafermionic topological states
• Manifestations of topological band crossings in bulk entanglement spectrum: An analytical study for integer quantum Hall states
• 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