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. We propose a machine learning approach that optimizes an effective model based on an estimation of its partition function. The success of the method is demonstrated by application to the single impurity Anderson model and double quantum dots, where nonperturbative results are obtained for the old problem of mapping to effective Kondo models. We also show that an alternative approach based on learning minimal models from observables may yield the wrong low-energy physics. On the other hand, learning minimal models from the partition function recovers the correct low-energy physics but may not reproduce all observables.