Chern insulator boundary criticality
Abstract
We investigate signatures of chirality at Chern insulator transitions in the presence of a boundary. The transition between a trivial insulator and a Chern insulator with Chern number C=1 is described by a massless Dirac fermion whose parity anomaly gives a critical Hall conductivity σxy=1/2e2/h. Using a Dirac mass domain wall construction, we show that the chiral edge mode delocalizes into the bulk at criticality, but the boundary fermion correlation function retains a chiral structure and acquires the scaling dimension of the bulk fermion. We compute current correlation functions and demonstrate that the anomaly of the bulk Hall response is matched by delocalized chiral modes near the boundary. Using only the residual conformal symmetry of a (2+1)d conformal field theory (CFT) in a half-space, we identify parity-odd terms in current and energy-momentum tensor correlation functions that encode these modes and determine their electromagnetic and gravitational anomaly coefficients. Our analysis therefore applies to general time-reversal breaking (2+1)d CFTs, beyond the free Dirac transition. In particular, the analysis of the gravitational anomaly is also applicable to the free Majorana CFT governing the transition between a trivial superconductor and a topological superconductor. We also extend our results to more general Chern number changing transitions and to the transition between a (3+1)d topological insulator and a trivial insulator.
Related
- Criticality and Quench Dynamics at the Anderson Transition of a Chern Insulator
- Chiral p-Wave Superconductivity Proximate to a Fractional Chern Insulator and a Topological Charge Density Wave in a Moiré Chern Band
- Vacancy-driven topological transition of a Chern insulator
- Dynamical transition in non-Hermitian Chern insulator
- Deconfined criticality between an antiferromagnetic insulator and a nodal d-wave superconductor: a quantum Monte Carlo study
BibTeX
@misc{moy2026chern,
title = {{Chern insulator boundary criticality}},
author = {Benjamin Moy and Eduardo Fradkin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.18199},
eprint = {2608.18199},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.18199},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Chern insulator boundary criticality
AU - Benjamin Moy
AU - Eduardo Fradkin
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2608.18199
UR - https://arxiv.org/abs/2608.18199
AB - We investigate signatures of chirality at Chern insulator transitions in the presence of a boundary. The transition between a trivial insulator and a Chern insulator with Chern number C=1 is described by a massless Dirac fermion whose parity anomaly gives a critical Hall conductivity σ_xy=1/2e^2/h. Using a Dirac mass domain wall construction, we show that the chiral edge mode delocalizes into the bulk at criticality, but the boundary fermion correlation function retains a chiral structure and acquires the scaling dimension of the bulk fermion. We compute current correlation functions and demonstrate that the anomaly of the bulk Hall response is matched by delocalized chiral modes near the boundary. Using only the residual conformal symmetry of a (2+1)d conformal field theory (CFT) in a half-space, we identify parity-odd terms in current and energy-momentum tensor correlation functions that encode these modes and determine their electromagnetic and gravitational anomaly coefficients. Our analysis therefore applies to general time-reversal breaking (2+1)d CFTs, beyond the free Dirac transition. In particular, the analysis of the gravitational anomaly is also applicable to the free Majorana CFT governing the transition between a trivial superconductor and a topological superconductor. We also extend our results to more general Chern number changing transitions and to the transition between a (3+1)d topological insulator and a trivial insulator.
ER -