Spectral Function Method and Janus Quantum Numbers in Quasiperiodic Systems
Abstract
The absence of translational symmetry in quasiperiodic systems invalidates conventional band theory, posing the central challenge in the field. Building upon the incommensurate energy band (IEB) concept, we establish a unified spectral theory for quasiperiodic systems by introducing two key advances. First, we develop an efficient spectral function method that calculates A(k,ω) using a small truncated Hamiltonian matrix, bypassing full diagonalization. It converges via a distinctive successive locking of energy moments, yielding exact thermodynamic-limit results without finite-size scaling. Second, we introduce that quasiperiodic eigenstates possess Janus quantum numbers: a single eigenstate, continuously tracked across localization transitions, carries dual labels in momentum and real space, which naturally reduce to the familiar Bloch momentum and band index in the commensurate limit. Together with IEB, these advances constitute a ``band theory'' for quasiperiodic systems, enabling us to define, compute, and label states with the same facility as in periodic ones.
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BibTeX
@misc{wu2026spectral,
title = {{Spectral Function Method and Janus Quantum Numbers in Quasiperiodic Systems}},
author = {Tian-Le Wu and Shi-Ping Ding and Miao Liang and Jing-Tao Lü and Jin-Hua Gao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03555},
eprint = {2609.03555},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03555},
}
RIS
TY - UNPB
TI - Spectral Function Method and Janus Quantum Numbers in Quasiperiodic Systems
AU - Tian-Le Wu
AU - Shi-Ping Ding
AU - Miao Liang
AU - Jing-Tao Lü
AU - Jin-Hua Gao
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03555
UR - https://arxiv.org/abs/2609.03555
AB - The absence of translational symmetry in quasiperiodic systems invalidates conventional band theory, posing the central challenge in the field. Building upon the incommensurate energy band (IEB) concept, we establish a unified spectral theory for quasiperiodic systems by introducing two key advances. First, we develop an efficient spectral function method that calculates A(k,ω) using a small truncated Hamiltonian matrix, bypassing full diagonalization. It converges via a distinctive successive locking of energy moments, yielding exact thermodynamic-limit results without finite-size scaling. Second, we introduce that quasiperiodic eigenstates possess Janus quantum numbers: a single eigenstate, continuously tracked across localization transitions, carries dual labels in momentum and real space, which naturally reduce to the familiar Bloch momentum and band index in the commensurate limit. Together with IEB, these advances constitute a ``band theory'' for quasiperiodic systems, enabling us to define, compute, and label states with the same facility as in periodic ones.
ER -