Acceleration of CTQMC via Denoising Diffusion Models with Auxiliary Spectral Functions

Abstract

Continuous-time Quantum Monte Carlo (CTQMC) impurity solvers are a numerically exact, but expensive, option for solving the Dynamical Mean Field Theory (DMFT) equations, with statistical noise from undersampling presenting a major challenge to low temperature studies. This noise is especially egregious within the sampled self-energy, which can destabilize the self-consistency loop upon insertion into the Dyson equation. In this work, we introduce a neural denoiser for fermionic imaginary time Green's functions based on the diffusion model architecture trained on synthetic data. The network predicts positive and normalized auxiliary spectral functions consistent with the noisy imaginary axis CTQMC data, which is then refined via autodifferentiation to match the measured self-energy, its first two high-frequency moments, and impurity occupation similar to the Constrained Residual Minimization (CRM) method. This leads to Green's functions and self-energies that are causal by design. Through this denoising framework we are able to reduce the required CTQMC measurement steps by a factor of 10-100. We benchmark our method with a half-filled Hubbard model on a Bethe lattice, a two-patch Dynamical Cluster Approximation (DCA) of the two-dimensional Hubbard model, and the SrVO$_3$ system. We reproduce the Mott transition upon increasing Coulomb interaction for the half-filled Hubbard model with only 5000 CTQMC measurements, the pseudogap transition for the DCA two-dimensional Hubbard model with only 5$\times$10$^5$ measurements, and match the spectral function of SrVO$_3$ with 50 times fewer measurements than the reference. Since we generate auxiliary spectral functions, we recover the approximate spectral functions of the systems for free without performing analytic continuation.