Speaker
Description
Configuration-space truncation is a basic step in quantum-selected configuration interaction and related sample-based diagonalization methods, but the number of basis configurations required to retain a prescribed fraction of a many-body state is generally unknown. We study this intrinsic truncation problem for the fixed-particle-number ground state of the periodic XX, or free-fermion, chain. Its occupation-basis Born probabilities form a discrete circular log gas. Interpreting $Y(X)=-\log p(X)$ as an effective configuration energy, we derive exact expressions at arbitrary fixed filling for its mean density $h(\rho)$, equal to the Shannon participation-entropy density, and its leading fluctuation density $v(\rho)$, equal to the varentropy density. We prove that $\frac{Y}{L}$ becomes self-averaging, with $\operatorname{Var}(Y)=L v(\rho)+o(L)$, so that asymptotically all Born weight is concentrated in a microcanonical-like configuration-energy shell around $Y\simeq Lh(\rho)$. Consequently, optimal truncation to the (M) most probable configurations has a sharp threshold at the level of exponential rates: the retained probability tends to zero when $L^{-1}\log M<h(\rho)$, and to one when $L^{-1}\log M>h(\rho)$. Our results provide an analytic benchmark for ideal support selection and connect wave-function truncation with participation entropy, log-gas thermodynamics, and information-density concentration.