Machine learning effective models for quantum systems*

The construction of good effective models is an essential part of understanding and simulating complex systems in many areas of science. It is a particular challenge for correlated many body quantum systems displaying emergent physics. Using information theoretic techniques, we propose a model machine learning approach that optimizes an effective model based on an estimation of its partition function. The success of the method is exemplified by application to the single impurity Anderson model and double quantum dots, with new non-perturbative results obtained for the old problem of mapping to effective Kondo models. We also show that the correct effective model is not in general obtained by attempting to match observables to those of its parent Hamiltonian, due to information monotonicity along RG flow.

[1] J. B. Rigo and A. K. Mitchell, arXiv:1910.11300