Nullspace-guided Adaptive Bootstrap of Quantum Many-body Systems
Abstract
We introduce a nullspace-guided adaptive (NGA) bootstrap method that improves the energy lower bounds of quantum many-body ground states by refining the bootstrap basis in a dynamic and incremental way. At each iteration, the optimized moment matrix reveals a nullspace of saturated positivity directions, which is intuitively interpreted as annihilators of the approximate ground-state subspace. The NGA bootstrap then prunes operators with small nullspace leverage and grows the basis along descendants of these null directions. By applying the NGA bootstrap to the transverse-field Ising chain, we obtain nearly exact energy lower bounds because the algorithm automatically discovers the eigenoperator structure in terms of Jordan-Wigner fermions from a minimal local bootstrap basis. For the Hubbard chain, it improves upon state-of-the-art energy lower bounds by up to two orders of magnitude, reaching errors ranging from 10−3 down to 10−5 in the strongly correlated regimes. We further show that the NGA framework can be used to improve the certified two-sided bounds on general observables. In addition, the bootstrap error decreases approximately as a power law with increasing computational resources. These results suggest that our method provides a practical and scalable route toward accurate bootstrap of general quantum many-body systems.
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BibTeX
@misc{wang2026nullspaceguided,
title = {{Nullspace-guided Adaptive Bootstrap of Quantum Many-body Systems}},
author = {Xu-Cheng Wang and Yang Qi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25834},
eprint = {2609.25834},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25834},
}
RIS
TY - UNPB
TI - Nullspace-guided Adaptive Bootstrap of Quantum Many-body Systems
AU - Xu-Cheng Wang
AU - Yang Qi
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.25834
UR - https://arxiv.org/abs/2609.25834
AB - We introduce a nullspace-guided adaptive (NGA) bootstrap method that improves the energy lower bounds of quantum many-body ground states by refining the bootstrap basis in a dynamic and incremental way. At each iteration, the optimized moment matrix reveals a nullspace of saturated positivity directions, which is intuitively interpreted as annihilators of the approximate ground-state subspace. The NGA bootstrap then prunes operators with small nullspace leverage and grows the basis along descendants of these null directions. By applying the NGA bootstrap to the transverse-field Ising chain, we obtain nearly exact energy lower bounds because the algorithm automatically discovers the eigenoperator structure in terms of Jordan-Wigner fermions from a minimal local bootstrap basis. For the Hubbard chain, it improves upon state-of-the-art energy lower bounds by up to two orders of magnitude, reaching errors ranging from 10^−3 down to 10^−5 in the strongly correlated regimes. We further show that the NGA framework can be used to improve the certified two-sided bounds on general observables. In addition, the bootstrap error decreases approximately as a power law with increasing computational resources. These results suggest that our method provides a practical and scalable route toward accurate bootstrap of general quantum many-body systems.
ER -