2026/04/02 by Ingvars Vitenburgs, Jarvist Moore Frost · 1 voice
#cond-mat.str-el #cond-mat.stat-mech
Some notable technology systems, such as high-temperature superconductors and materials for controlled nuclear fusion, require an accurate description of finite-temperature quantum matter. Stochastic path integral methods are finite-temperature and numerically exact, but scale poorly with system size due the notorious Fermion sign problem. To somewhat mitigate this, we use a hydrodynamical backflow coordinate transformation. Our first approach was a continuous normalizing flow machine learning optimisation. We found this to roughly halve the statistical uncertainty at medium sign severity. Numerical issues challenged training effectively. Thus, a semi-analytic analogue was developed to estimate the optimal parameters. We do this by using a derived expression dependent on a Bosonic observable. Hence, the calculation of these values does not have a sign problem. The resulting backflow transformations reduce the problem by multiple orders of magnitude in the specific case of a harmonically trapped, two-dimensional, electron gas at finite-temperature. The total energy of the system agrees with previous, backflow untransformed, studies and we calculate energies for up to 32 electrons. The limiting factor is found to be, primarily, the O(N3) calculation of the Jacobian, stemming from the coordinate transformation of the backflow. A more thorough implementation may further improve this scaling. Even without this, a route for simulating electron systems at currently unreachable regimes is obtained.