摘要：
Quantum many-body bootstrap is a nonperturbative method that uses positivity of operator correlation matrices together with consistency conditions, such as equations of motion, to constrain the spectra and observables of quantum many-body systems. In this talk, I will introduce a nullspace-guided adaptive (NGA) bootstrap that dynamically refines the bootstrap basis to improve ground-state energy lower bounds. At each iteration, the nullspace of the optimized moment matrix reveals annihilators of the approximate ground state; NGA prunes small-leverage operators and grows the basis along their descendants. For the transverse-field Ising chain, it gives nearly exact lower bounds by automatically discovering Jordan-Wigner fermionic eigenoperators from a minimal local basis. For the Hubbard chain, it improves state-of-the-art lower bounds by up to two orders of magnitude, reaching errors of 10^{-3} to 10^{-5} in strongly correlated regimes. It also sharpens certified two-sided bounds for general observables, with bootstrap error scaling as a power law with computational resources—offering a practical, scalable route to accurate quantum many-body bootstrap.