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

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Original abstract

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.

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• Official / arXiv page
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