Spindrift: Learning quantum degeneracy from thermal purity in restricted path integral Monte Carlo

Restricted path integral Monte Carlo (RPIMC) sidesteps the fluctuating Fermion sign problem by confining paths within nodal pockets of a trial density matrix, thereby recovering polynomial scaling. However, this nodal surface must be provided from elsewhere; unless it is exact, it introduces a fixed-node energy error. Here we introduce \textsc{Spindrift}, a Variational Density Matrix approach that learns the many-body Fermionic density matrix from a regularised Bloch residual, evaluated on samples drawn by a restricted Worm algorithm. Motivated by the observation of the `purity' of quantum mechanics at high temperature (where kinetic energy dominates), we train the density matrix along a temperature (imaginary time) curriculum, learning increasingly large \emph{corrections} to the initial free-particle reference. We parametrise our model with a permutation-equivariant continuous normalising flow to generate quasi-particle backflow trajectories, modulated by a symmetric Jastrow factor. This architecture guarantees exact Fermionic antisymmetry and spatial symmetry throughout training. Simulating $N=3$ interacting Fermions in a two-dimensional harmonic trap, we demonstrate stable curriculum training. The learnt velocity field smoothly deforms the nodal structure away from the free-particle reference. Open-Worm G-sector trapping provides a natural diagnostic for nodal accuracy. Although the current lack of a nodal action in our estimator precludes absolute benchmarking, \textsc{Spindrift} lowers the restricted thermodynamic energy relative to the free-particle reference at each temperature, establishing a stable, physics-informed framework for finite-temperature quantum Monte Carlo where the nodal structure is learnt self-consistently.