Gauge-covariant magnetic Bloch sums for general multiorbital Hofstadter models
Abstract
We formulate a unified treatment of the Hofstadter problem for general two-dimensional multiorbital Peierls tight-binding Hamiltonians using a gauge-covariant magnetic Bloch-sum basis. The construction retains the full Bravais geometry, arbitrary intracell orbital positions, and the original hopping table, so lattice geometry, orbital embedding, hopping range, and orbital content can all be handled within the same framework. At rational flux Φ/Φ0=p/q, commuting magnetic translations reduce the Peierls Hamiltonian to minimal qNorb× qNorb blocks. Their dimension depends only on the flux through the primitive cell, even when the fractional orbital coordinates are irrational. Electromagnetic gauge transformations act by unitary conjugation within the construction and do not alter the required magnetic supercell. We derive an explicit sparse matrix in an oblique Landau gauge and establish the associated band counting, spectral redundancy, Chern-number formulation, magnetic spatial constraints, and flux periodicity. Numerical examples include elementary lattices, topological and flat-band models, and a spinful 22-band Wannier Hamiltonian of monolayer MoS2, demonstrating a direct interface with first-principles electronic-structure calculations. As a complementary representation, we also derive exact generalized Harper equations from the same hopping data and relate them to the finite magnetic-Bloch blocks.
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BibTeX
@misc{shi2026gaugecovariant,
title = {{Gauge-covariant magnetic Bloch sums for general multiorbital Hofstadter models}},
author = {Hao Shi and Tianyu Qiao and Wangqian Miao and Jin-Tao Jin and Quansheng Wu and Xi Dai},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05646},
eprint = {2609.05646},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05646},
}
RIS
TY - UNPB
TI - Gauge-covariant magnetic Bloch sums for general multiorbital Hofstadter models
AU - Hao Shi
AU - Tianyu Qiao
AU - Wangqian Miao
AU - Jin-Tao Jin
AU - Quansheng Wu
AU - Xi Dai
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.05646
UR - https://arxiv.org/abs/2609.05646
AB - We formulate a unified treatment of the Hofstadter problem for general two-dimensional multiorbital Peierls tight-binding Hamiltonians using a gauge-covariant magnetic Bloch-sum basis. The construction retains the full Bravais geometry, arbitrary intracell orbital positions, and the original hopping table, so lattice geometry, orbital embedding, hopping range, and orbital content can all be handled within the same framework. At rational flux Φ/Φ_0=p/q, commuting magnetic translations reduce the Peierls Hamiltonian to minimal qN_orb× qN_orb blocks. Their dimension depends only on the flux through the primitive cell, even when the fractional orbital coordinates are irrational. Electromagnetic gauge transformations act by unitary conjugation within the construction and do not alter the required magnetic supercell. We derive an explicit sparse matrix in an oblique Landau gauge and establish the associated band counting, spectral redundancy, Chern-number formulation, magnetic spatial constraints, and flux periodicity. Numerical examples include elementary lattices, topological and flat-band models, and a spinful 22-band Wannier Hamiltonian of monolayer MoS_2, demonstrating a direct interface with first-principles electronic-structure calculations. As a complementary representation, we also derive exact generalized Harper equations from the same hopping data and relate them to the finite magnetic-Bloch blocks.
ER -