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

TL;DR

This paper uncovers topologically distinct critical theories for quantum Hall phase transitions by analyzing the bulk entanglement spectrum, revealing new gapless excitations and fractionalized states without fine tuning.

Contribution

It introduces a novel method to derive critical theories from the bulk entanglement spectrum, highlighting differences between $ u=1$ and $ u=2$ states and establishing a topological correspondence.

Findings

For $ u=1$, the critical theory has a Dirac cone spectrum with fractionalized zero-energy states.

For $ u=2$, the critical theory shows a parabolic spectrum without fractionalization.

A bulk-edge-critical correspondence is demonstrated via the entanglement spectrum.

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.