Abstract
The coherent superposition of nonorthogonal fermionic Gaussian states has been shown to be an efficient approximation to the ground states of quantum impurity problems [Bravyi and Gosset, Commun. Math. Phys. 356, 451 (2017)]. We propose 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.
Highlights
Quantum impurity models—systems of a few strongly interacting degrees of freedom coupled to a large bath of noninteracting fermions—constitute an important class of problems in condensed matter physics
We find that using comparable computational resources, our method is able to achieve an error in the ground-state energy that is about one order of magnitude better than density matrix renormalization group (DMRG)
The SGS ansatz considered in this paper can be seen as a generalization of the generalized Hartree-Fock (GHF) method [22,23], which aims to find the approximate ground state of a system using a variational minimization over the field of fermionic Gaussian states
Summary
Quantum impurity models—systems of a few strongly interacting degrees of freedom coupled to a large bath of noninteracting fermions—constitute an important class of problems in condensed matter physics. A natural question is whether a well-chosen class of variational states could exploit the structure of quantum impurity models to circumvent the limitations of these established approaches. [12] demonstrate that the minimal rank to obtain a good approximation of the ground state scales only with the size of the impurity and the desired precision, while being independent of the size of the bath Having chosen this superposition of Gaussians (SGS) ansatz for the study of quantum impurity models, the challenge is to devise practical algorithms to perform numerically efficient computations. The SGS ansatz considered in this paper can be seen as a generalization of the generalized Hartree-Fock (GHF) method [22,23], which aims to find the approximate ground state of a system using a variational minimization over the field of fermionic Gaussian states. V we extend the calculations of the previous section by considering the twochannel Kondo model
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