Non-Gaussian variational approach to Fermi polarons in one- and two-dimensional lattices

Liu, Ruijin; Shi, Yue-Ran; Zhang, Wei

doi:10.1103/physreva.102.033305

Cited by 8 publications

(4 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To evolve the variational parameter γ according to EOM given by equation ( 14), we need to calculate the functional derivative h defined in equation (13). To accomplish that, we first rewrite the Hamiltonian equation ( 2) with Majorana operators…”

Section: Hamiltonian and Gaussian Variational Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Gaussian variational method to Fermi-Hubbard model in one and two dimensions

Shi,

He,

Liu

et al. 2023

New J. Phys.

View full text Add to dashboard Cite

The study of ground-state properties of the Fermi-Hubbard model is a long-lasting task in the research of strongly correlated systems, and is crucial for the understanding of notable quantum phenomena including superconductivity and magnetism. Owing to the exponentially growing complexity of the system, a quantitative analysis usually demands high computational cost and is restricted to small samples, especially in two or higher dimensions. Here, we introduce a variational method in the frame of fermionic Gaussian states, and obtain the ground states of one- and two-dimensional attractive Hubbard models via imaginary-time evolution. We calculate the total energy and benchmark the results in a wide range of interaction strength and ﬁlling factor with those obtained via exact two-body results, the density matrix renormalization group based on matrix product states (MPS), and projector Quantum Monte Carlo (QMC) method. For both 1D and 2D cases, the Gaussian variational method presents accurate results for total energy with a maximum systematic error ∼ 4% in the intermediate interaction region. The accuracy of these results has negligible dependence on the system size. We further calculate the double occupancy and ﬁnd excellent agreement with MPS and QMC, as well as the experimental results of cold quantum gases in optical lattices. The results suggest that the Gaussian pairing state is a good approximation to the ground states of attractive Hubbard model, in particular in the strong and weak coupling limits. Moreover, we generalize the method to the attractive Hubbard model with a ﬁnite spin-polarization, which can be mapped to the repulsive interaction case via particle-hole transformation, and obtain accurate results of ground state energy and double occupancy. Our work demonstrates the ability of the Gaussian variational method to extract ground state properties of strongly correlated many-body systems with negligible computational cost, especially of large size and in higher dimensions.

show abstract

Section: Hamiltonian and Gaussian Variational Methodsmentioning

confidence: 99%

“…Further improvement of the method via appropriate canonical transformations is also available. Moreover, by extending Gaussian states to generalized non-Gaussian forms [12][13][14], richer and more accurate variational solutions can be obtained, even for Bose-Fermi mixed systems.…”

Section: Introductionmentioning

confidence: 99%

Gaussian variational method to Fermi-Hubbard model in one and two dimensions

Shi,

He,

Liu

et al. 2023

New J. Phys.

View full text Add to dashboard Cite

show abstract

“…We will refer to the method employed by Shi et al as the variational method. Since then, a number of works have used this variational method in order to classically simulate various spin-, bosonic-, and fermionic systems [26][27][28][29][30][31][32][33][34][35][36]. However, to the best of our knowledge, no work has so far applied the variational method of Shi et al to optimize the non-Gaussian part for strongly correlated purely fermionic systems.…”

Section: Introductionmentioning

confidence: 99%

Algorithm for initializing a generalized fermionic Gaussian state on a quantum computer

Kaicher¹,

Jäger²,

Wilhelm³

2021

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

We present explicit expressions for the central piece of a variational method developed by Shi et al (2018 Ann. Phys. 390 245) which extends variational wave functions that are efficiently computable on classical computers beyond mean-field to generalized Gaussian states. In particular, we derive iterative analytical expressions for the evaluation of expectation values of products of fermionic creation and annihilation operators in a Grassmann variable-free representation. Using this result we find a closed expression for the energy functional and its gradient of a general fermionic quantum many-body Hamiltonian. We present a simple gradient-descent-based algorithm that can be used as an optimization subroutine in combination with imaginary time evolution, which by construction guarantees a monotonic decrease of the energy in each iteration step. Due to the simplicity of the quantum circuit implementing the variational state ansatz, the results of the algorithms discussed here and in Shi et al’s work could serve as an improved, beyond mean-field initial state in quantum computation.

show abstract

“…To further consider polaron decay, the diagrammatic many-body method is implemented to give the polaron self-energy with ladder diagram approximation [48,49]. The fixednode quantum Monte Carlo (QMC) algorithm [50][51][52], the imaginary lattice quantum Monte Carlo (ILMC) [53], the functional renormalization group [54], and the non-Gaussian variational method [55] have also been adopted to analyze this topic. However, impurity in a dissipative bath has not been studied so far to the best of our knowledge.…”

mentioning

confidence: 99%

Fermi polaron in dissipative bath with spin-orbit coupling

Zhou¹,

Zhang²

2021

EPL

View full text Add to dashboard Cite

We study the polaron problem of an impurity immersed in a dissipative spin-orbit coupled Fermi gas via a non-self-consistent T -matrix method. We first propose an experimental scheme to realize a spin-orbit coupled Fermi bath with dissipation, and show that such a system can be described by a non-Hermitian Hamiltonian that contains an imaginary spin-flip term and an imaginary constant shift term. We find that the non-Hermiticity will change the single-particle dispersion of the bath gas, and modify the properties of attractive and repulsive polarons such as energy, quasi-particle residue, effective mass, and decay rate. We also investigate the Thouless criteria corresponding to the instability of the polaron-molecule transition, which suggests a molecule state is more facilitated with stronger bath dissipation. Finally, we consider the case with finite impurity density and calculate the interaction between polarons. Our result extends the study of polaron physics to non-Hermitian systems and may be realized in future experiments.

show abstract

Non-Gaussian variational approach to Fermi polarons in one- and two-dimensional lattices

Cited by 8 publications

References 47 publications

Gaussian variational method to Fermi-Hubbard model in one and two dimensions

Gaussian variational method to Fermi-Hubbard model in one and two dimensions

Algorithm for initializing a generalized fermionic Gaussian state on a quantum computer

Fermi polaron in dissipative bath with spin-orbit coupling

Contact Info

Product

Resources

About