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The coherent superposition of non-orthogonal fermionic Gaussian states hasbeen shown to be an efficient approximation to the ground states of quantumimpurity problems [Bravyi and Gosset,Comm. Math. Phys.,356 451 (2017)]. Wepresent a practical approach for performing a variational calculation based onsuch states. Our method is based on approximate imaginary-time equations ofmotion that decouple the dynamics of each Gaussian state forming the ansatz. Itis independent of the lattice connectivity of the model and the implementationis highly parallelizable. To benchmark our variational method, we calculate thespin-spin correlation function and R\'enyi entanglement entropy of an Andersonimpurity, allowing us to identify the screening cloud and compare to densitymatrix renormalization group calculations. Secondly, we study the screeningcloud of the two-channel Kondo model, a problem difficult to tackle usingexisting numerical tools.

Quantum impurity models using superpositions of fermionic Gaussian states: Practical methods and applications