Full Uncertainty Quantification of Sign-Problem-Free Quantum Monte Carlo Methods and Nuclear Lattice Effective Field Theory Benchmarks

Abstract

Sign-problem-free quantum Monte Carlo (QMC) methods provide one of the few polynomial-scaling routes to controlled, nonperturbative benchmarks of medium-mass and heavy nuclei. We present a detailed uncertainty analysis of the recently developed sign-problem-free spin-orbit lattice action LAT-OPT1 and use it to benchmark nuclear lattice effective field theory (NLEFT). We quantify various systematic uncertainties, finding that the cumulative many-body computational uncertainty in ground-state energies of doubly magic nuclei up to $^{100}$Sn is well below the percent level. In response to recent criticism of NLEFT benchmarks, we also revisit the relation between lattice transfer matrices, lattice Hamiltonians, Hartree--Fock variational bounds, finite-box and thermodynamic-limit calculations, and the continuum-limit behavior of regulated lattice interactions. We identify several conceptual and technical errors in the analysis of Ref.~\cite{Rothman2026_NuLattice}. These include (i) the comparison of inequivalent lattice transfer-matrix and lattice-Hamiltonian calculations, (ii) an inconsistent determination of correlation energies from comparisons of Hartree--Fock and full ground-state calculations with different boundary conditions, (iii) the attribution of nuclear saturation to lattice artifacts rather than to nonlocal smearing of interactions, a mechanism that can be demonstrated in continuous space, and (iv) an incorrect renormalization of short-range two-body interactions in the continuum limit. When the same regulated lattice theory, renormalization prescription, and finite-volume boundary conditions are used consistently and analyzed properly, the reported discrepancies and concerns about the corresponding published NLEFT results are resolved.