IDMate: Finite-temperature error bounds for window-resolved self-consistent-field screening
Abstract
We formulate a finite-temperature residual test in IDMate that bounds window-resolved electronic errors without a spectral-gap assumption. For a fixed Hamiltonian and exact electron number, strong convexity of the matrix Fermi entropy bounds the density-matrix distance and free-energy error within a selected window. The bound remains finite at spectral crossings and extends to weighted k points with a shared chemical potential. We also derive a distance correction for particle-number mismatch. Across 3,586 stress trials in $70$ seeded perturbation ladders, 1,942 proposals satisfy the screen with no observed violation of the $0.05$ window-distance criterion plus its numerical allowance. This criterion differs from the uncorrected exact-trace bound, which six of ten historical in-loop candidates exceed at the numerical-error scale. An accept-or-recover loop replaces ten reference-map evaluations while meeting terminal comparison criteria in three configurations that include oracle-subspace controls. Additional candidates built only from preceding-iteration orbitals yield two acceptances and one abstention. The silicon candidate has a window distance of 1.891×10−13 but a normalized real-space density error of 3.754%. Analytic examples separate errors from complement occupations and interblock coupling. Window-level accuracy therefore does not imply full-state accuracy; the screen tests compressed proposal quality, independently of nonlinear SCF convergence or net acceleration.
Related
- Towards a consistent perturbation theory at finite temperature
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BibTeX
@misc{kang2026idmate,
title = {{IDMate: Finite-temperature error bounds for window-resolved self-consistent-field screening}},
author = {Peng Kang and Da Wan and Shulin Bai and Zhen Li and Yu Liu and Lei Zheng and Li-Dong Zhao and Huibin Xu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02979},
eprint = {2609.02979},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02979},
}
RIS
TY - UNPB
TI - IDMate: Finite-temperature error bounds for window-resolved self-consistent-field screening
AU - Peng Kang
AU - Da Wan
AU - Shulin Bai
AU - Zhen Li
AU - Yu Liu
AU - Lei Zheng
AU - Li-Dong Zhao
AU - Huibin Xu
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.02979
UR - https://arxiv.org/abs/2609.02979
AB - We formulate a finite-temperature residual test in IDMate that bounds window-resolved electronic errors without a spectral-gap assumption. For a fixed Hamiltonian and exact electron number, strong convexity of the matrix Fermi entropy bounds the density-matrix distance and free-energy error within a selected window. The bound remains finite at spectral crossings and extends to weighted k points with a shared chemical potential. We also derive a distance correction for particle-number mismatch. Across 3,586 stress trials in $70$ seeded perturbation ladders, 1,942 proposals satisfy the screen with no observed violation of the $0.05$ window-distance criterion plus its numerical allowance. This criterion differs from the uncorrected exact-trace bound, which six of ten historical in-loop candidates exceed at the numerical-error scale. An accept-or-recover loop replaces ten reference-map evaluations while meeting terminal comparison criteria in three configurations that include oracle-subspace controls. Additional candidates built only from preceding-iteration orbitals yield two acceptances and one abstention. The silicon candidate has a window distance of 1.891×10^−13 but a normalized real-space density error of 3.754%. Analytic examples separate errors from complement occupations and interblock coupling. Window-level accuracy therefore does not imply full-state accuracy; the screen tests compressed proposal quality, independently of nonlinear SCF convergence or net acceleration.
ER -