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.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.

arXiv:2105.01088Physical Review ResearchAug 24, 20219 citations

Variational approach to the dynamics of dissipative quantum impurity models

Yi-Fan Qu, Martino Stefanini, Tao Shi +4 more

Simulating dissipative quantum many-body systems presents a significant theoretical challenge. Here, the authors develop an efficient nonperturbative framework that is tailored to dissipative impurity problems, combining a superposition of Gaussian states (SGS) variational ansatz with the quantum trajectory approach. They showcase the method with a model of a spinful impurity subject to two-body losses embedded in a fermionic bath, for which they explore the full crossover from weak to strong dissipation. Their approach captures the emergence of a loss-induced Kondo effect under strong dissipation, and reveals an exotic negative conductance phenomenon at intermediate loss rates.Simulating dissipative quantum many-body systems presents a significant theoretical challenge. Here, the authors develop an efficient nonperturbative framework that is tailored to dissipative impurity problems, combining a superposition of Gaussian states (SGS) variational ansatz with the quantum trajectory approach. They showcase the method with a model of a spinful impurity subject to two-body losses embedded in a fermionic bath, for which they explore the full crossover from weak to strong dissipation. Their approach captures the emergence of a loss-induced Kondo effect under strong dissipation, and reveals an exotic negative conductance phenomenon at intermediate loss rates.

arXiv:2411.13638Physical review. B./Physical review. BApr 8, 202512 citations

Hybrid quantum-classical algorithms for quantum impurity problems

理人櫻井

Mar 1, 20240 citations

Efficient impurity-bath trial states from superposed Slater determinants

Izak Snyman, Serge Florens

The representation of ground states of fermionic quantum impurity problems as superpositions of Gaussian states has recently been given a rigorous mathematical foundation [S. Bravyi and D. Gosset, Commun. Math. Phys. 356, 451 (2017)]. It is natural to ask how many parameters are required for an efficient variational scheme based on this representation. An upper bound is $O({N}^{2})$ , where $N$ is the system size, which corresponds to the number parameters needed to specify an arbitrary Gaussian state. We provide an alternative representation, with more favorable scaling, only requiring $O(N)$ parameters, that we illustrate for the interacting resonant-level model. We achieve the reduction by associating mean-field-like parent Hamiltonians with the individual terms in the superposition, using physical insight to retain only the most relevant channels in each parent Hamiltonian. We benchmark our variational ansatz against the numerical renormalization group, and compare our results to other variational schemes of a similar nature to ours. Apart from the ground-state energy, we also study the spectrum of the covariance matrix---a very stringent measure of accuracy. Our approach outperforms some existing variational schemes and remains quantitatively accurate in the numerically challenging near-critical regime.The representation of ground states of fermionic quantum impurity problems as superpositions of Gaussian states has recently been given a rigorous mathematical foundation [S. Bravyi and D. Gosset, Commun. Math. Phys. 356, 451 (2017)]. It is natural to ask how many parameters are required for an efficient variational scheme based on this representation. An upper bound is $O({N}^{2})$, where $N$ is the system size, which corresponds to the number parameters needed to specify an arbitrary Gaussian state. We provide an alternative representation, with more favorable scaling, only requiring $O(N)$ parameters, that we illustrate for the interacting resonant-level model. We achieve the reduction by associating mean-field-like parent Hamiltonians with the individual terms in the superposition, using physical insight to retain only the most relevant channels in each parent Hamiltonian. We benchmark our variational ansatz against the numerical renormalization group, and compare our results to other variational schemes of a similar nature to ours. Apart from the ground-state energy, we also study the spectrum of the covariance matrix---a very stringent measure of accuracy. Our approach outperforms some existing variational schemes and remains quantitatively accurate in the numerically challenging near-critical regime.

arXiv:2106.14027Physical review. B./Physical review. BNov 19, 20215 citations

Hermite–Gaussian model for quantum states

Marcelo Losada, Ignacio S. Gomez, Federico Holik

arXiv:1811.01207Physica A Statistical Mechanics and its ApplicationsJun 19, 20191 citation

O({N}^{2})

, where

N

is the system size, which corresponds to the number parameters needed to specify an arbitrary Gaussian state. We provide an alternative representation, with more favorable scaling, only requiring

O(N)

parameters, that we illustrate for the interacting resonant-level model. We achieve the reduction by associating mean-field-like parent Hamiltonians with the individual terms in the superposition, using physical insight to retain only the most relevant channels in each parent Hamiltonian. We benchmark our variational ansatz against the numerical renormalization group, and compare our results to other variational schemes of a similar nature to ours. Apart from the ground-state energy, we also study the spectrum of the covariance matrix---a very stringent measure of accuracy. Our approach outperforms some existing variational schemes and remains quantitatively accurate in the numerically challenging near-critical regime.