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

TL;DR

This paper introduces a practical variational method using superpositions of fermionic Gaussian states to efficiently approximate ground states of quantum impurity models, enabling analysis of complex phenomena like the Kondo effect.

Contribution

It develops a new variational approach based on imaginary-time equations of motion for superpositions of fermionic Gaussian states, applicable regardless of lattice connectivity and highly parallelizable.

Findings

Successfully benchmarked on Anderson impurity model with correlation functions and entanglement entropy.

Analyzed the screening cloud in the two-channel Kondo model, a challenging problem for existing methods.

Abstract

The coherent superposition of non-orthogonal fermionic Gaussian states has been shown to be an efficient approximation to the ground states of quantum impurity problems [Bravyi and Gosset,Comm. Math. Phys.,356 451 (2017)]. We present a practical approach for performing a variational calculation based on such states. Our method is based on approximate imaginary-time equations of motion that decouple the dynamics of each Gaussian state forming the ansatz. It is independent of the lattice connectivity of the model and the implementation is highly parallelizable. To benchmark our variational method, we calculate the spin-spin correlation function and R\'enyi entanglement entropy of an Anderson impurity, allowing us to identify the screening cloud and compare to density matrix renormalization group calculations. Secondly, we study the screening cloud of the two-channel Kondo model, a problem difficult to tackle using existing numerical tools.