Maximally Localized Dynamical Quantum Embedding for Solving Many-Body Correlated Systems

TL;DR

This paper introduces a quantum embedding method that efficiently models many-body correlated systems, accurately capturing phenomena like the Mott transition and Kondo physics with fewer bath sites, suitable for quantum computing applications.

Contribution

The authors develop a maximally localized dynamical quantum embedding approach that enhances the description of correlated systems with minimal non-local correlation components.

Findings

Reproduces Mott transition and Kondo physics with only 3 bath sites.

Provides excellent agreement for dynamical magnetic susceptibilities.

Offers a polynomial increase in degrees of freedom without additional bath sites.

Abstract

We present a quantum embedding methodology to resolve the Anderson impurity model in the context of dynamical mean-field theory, based on an extended exact diagonalization method. Our method provides a maximally localized quantum impurity model, where the non-local components of the correlation potential remain minimal. This method comes at a large benefit, as the environment used in the quantum embedding approach is described by propagating correlated electrons and hence offers a polynomial increase $O(N^4)$ of the number of degrees of freedom for the embedding mapping without adding bath sites. We report that quantum impurity models with as few as 3 bath sites can reproduce both the Mott transition and the Kondo physics, thus opening a more accessible route to the description of time-dependent phenomena. Finally, we obtain excellent agreement for dynamical magnetic susceptibilities, poising this approach as a candidate to describe 2-particle excitations such as excitons in correlated systems. We expect that our approach will be highly beneficial for the implementation of embedding algorithms on quantum computers, as it allows for a fine description of the correlation in materials with a reduced number of required qubits.