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.

Strongly Correlated Electrons (cond-mat.str-el); Quantum Physics (quant-ph)

arXiv:2609.25834 [cond-mat.str-el]

(or arXiv:2609.25834v1 [cond-mat.str-el] for this version)

https://doi.org/10.48550/arXiv.2609.25834 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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