Unsupervised Model Learning for Quantum Impurity Systems
arxiv(2024)
摘要
Generalized quantum impurity models – which feature a few localized and
strongly-correlated degrees of freedom coupled to itinerant conduction
electrons – describe diverse physical systems, from magnetic moments in metals
to nanoelectronics quantum devices such as quantum dots or single-molecule
transistors. Correlated materials can also be understood as self-consistent
impurity models through dynamical mean field theory. Accurate simulation of
such models is challenging, especially at low temperatures, due to many-body
effects from electronic interactions, resulting in strong renormalization. In
particular, the interplay between local impurity complexity and Kondo physics
is highly nontrivial. A common approach, which we further develop in this work,
is to consider instead a simpler effective impurity model that still captures
the low-energy physics of interest. The mapping from bare to effective model is
typically done perturbatively, but even this can be difficult for complex
systems, and the resulting effective model parameters can anyway be quite
inaccurate. Here we develop a non-perturbative, unsupervised machine learning
approach to systematically obtain low-energy effective impurity-type models,
based on the renormalization group framework. The method is shown to be general
and flexible, as well as accurate and systematically improvable. We benchmark
the method against exact results for the Anderson impurity model, and provide
an outlook for more complex models beyond reach of existing methods.
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