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Semiclassical Band Splitting in the Infinite Chern Band Model
Abstract
We study the two lowest Bloch bands of the infinite Chern band model of Tan and Devakul in the semiclassical limit. When the Berry curvature parameter is an odd multiple of π, we show that the first two bands are exponentially close and meet at exactly one Dirac point. The proof combines Agmon estimates and WKB approximations for a matrix Schrödinger operator whose lowest potential eigenvalue has two wells. Geometric properties of the Agmon distance allow us to compute the leading tunneling coefficients by the method of stationary phase. We provide numerical computations to illustrate the asymptotic formula and support the conjecture that the two bands remain separated for other values of the Berry curvature parameter.
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BibTeX
@misc{guo2026semiclassical,
title = {{Semiclassical Band Splitting in the Infinite Chern Band Model}},
author = {Tyler Guo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21462},
eprint = {2610.21462},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21462},
}
RIS
TY - UNPB
TI - Semiclassical Band Splitting in the Infinite Chern Band Model
AU - Tyler Guo
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.21462
UR - https://arxiv.org/abs/2610.21462
AB - We study the two lowest Bloch bands of the infinite Chern band model of Tan and Devakul in the semiclassical limit. When the Berry curvature parameter is an odd multiple of π, we show that the first two bands are exponentially close and meet at exactly one Dirac point. The proof combines Agmon estimates and WKB approximations for a matrix Schrödinger operator whose lowest potential eigenvalue has two wells. Geometric properties of the Agmon distance allow us to compute the leading tunneling coefficients by the method of stationary phase. We provide numerical computations to illustrate the asymptotic formula and support the conjecture that the two bands remain separated for other values of the Berry curvature parameter.
ER -