Active learning approach to quantum embedding simulations of strongly correlated matter*

We present a new method for solving efficiently quantum embedding (QE) simulations of strongly correlated matter, based on probabilistic machine learning (ML). Our strategy consists in training a machine for bypassing the most computationally expensive components of QE algorithms, which is the calculation of the ground-state density matrix of the so-called “embedding Hamiltonian” (EH).  Rather than pre-training our machine, as in previous work [1], our method actively trains the ML algorithm on the fly. This allows us to reduce substantially the number of necessary training data, by computing only data corresponding to physically relevant embeddings. We benchmark our method on the recently developed ghost Gutzwiller approximation (g-GA) [2-4], showing that our ML algorithm efficiently exploits previously acquired data for reducing the computational cost of new computations, providing us with very reliable and accurate predictions.

[1] "Bypassing the computational bottleneck of quantum-embedding theories for strong electron correlations with machine learning", Phys. Rev. Res. 3, 013101 (2021). 

[2] "Emergent Bloch Excitations in Mott Matter", Phys. Rev. B 96, 195126 (2017).

[3] "Quantum-embedding description of the Anderson lattice model with the ghost Gutzwiller Approximation", Phys. Rev. B 104, L081103 (Letter) (2021).

[4] "Operatorial formulation of the ghost rotationally-invariant slave-Boson theory", Phys. Rev. B 105, 045111 (2022).