Variational ground states of the two-dimensional Hubbard model

Baeriswyl, D.; Eichenberger, David; Menteshashvili, M.

doi:10.1088/1367-2630/11/7/075010

Cited by 47 publications

(50 citation statements)

References 65 publications

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“…The results (86), (87), and (91) can also be obtained via other approaches, such as the spin density wave ansatz [101] (which is related to dynamical mean field theory according to Ref. [102]).…”

Section: B Quantum Depletionmentioning

confidence: 88%

Equilibration and prethermalization in the Bose-Hubbard and Fermi-Hubbard models

et al. 2014

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Section: B Quantum Depletionmentioning

confidence: 88%

Equilibration and prethermalization in the Bose-Hubbard and Fermi-Hubbard models

et al. 2014

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“…From a practical point of view, approximate methods should offer a good compromise between accuracy and computational cost. Many methods are available to tackle the strong-correlation problem; they include quantum and variational Monte Carlo [7][8][9][10][11][12], dynamical mean-field theory (DMFT) [13][14][15][16][17][18][19][20][21][22], density matrix renormalization group (DMRG) [23][24][25][26], methods based on symmetry breaking and restoration [27][28][29][30][31][32], and methods based on a Gutzwiller variational approach [33,34]. This list is not, by any means, exhaustive.…”

Section: Introductionmentioning

confidence: 99%

Density matrix embedding from broken symmetry lattice mean fields

Bulik

Scuseria²,

Dukelsky³

2014

Phys. Rev. B

125

210

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Several variants of the recently proposed density matrix embedding theory (DMET) [G. Knizia and G. K-L. Chan, Phys. Rev. Lett. 109, 186404 (2012)] are formulated and tested. We show that spin symmetry breaking of the lattice mean-field allows precise control of the lattice and fragment filling while providing very good agreement between predicted properties and exact results. We present a rigorous proof that at convergence this method is guaranteed to preserve lattice and fragment filling. Differences arising from fitting the fragment one-particle density matrix alone versus fitting fragment plus bath are scrutinized. We argue that it is important to restrict the density matrix fitting to solely the fragment. Furthermore, in the proposed broken symmetry formalism, it is possible to substantially simplify the embedding procedure without sacrificing its accuracy by resorting to density instead of density matrix fitting. This simplified density embedding theory (DET) greatly improves the convergence properties of the algorithm.

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“…JastrowGutzwiller correlation factors are also very popular as variational wave functions in quantum Monte Carlo and other applications [7][8][9][10][11][12][13][14][15]. Non-variational solutions have also been discussed in the literature.…”

mentioning

confidence: 99%

Lie algebraic similarity transformed Hamiltonians for lattice model systems

et al. 2015

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We present a class of Lie algebraic similarity transformations generated by exponentials of twobody on-site hermitian operators whose Hausdorff series can be summed exactly without truncation. The correlators are defined over the entire lattice and include the Gutzwiller factor n i↑ n i↓ , and twosite products of density (n i↑ + n i↓ ) and spin (n i↑ − n i↓ ) operators. The resulting non-hermitian many-body Hamiltonian can be solved in a biorthogonal mean-field approach with polynomial computational cost. The proposed similarity transformation generates locally weighted orbital transformations of the reference determinant. Although the energy of the model is unbound, projective equations in the spirit of coupled cluster theory lead to well-defined solutions. The theory is tested on the 1D and 2D repulsive Hubbard model where it yields accurate results for small and medium size interaction strengths.Introduction.-Hamiltonian similarity transformations are ubiquitous in many areas of physics, including electronic structure and condensed matter theories, and have been applied in a myriad of contexts [1][2][3][4][5][6]. JastrowGutzwiller correlation factors are also very popular as variational wave functions in quantum Monte Carlo and other applications [7][8][9][10][11][12][13][14][15]. Non-variational solutions have also been discussed in the literature. Tsuneyuki [16] presented a Hilbert space Jastrow method based on a Gutzwiller factor i n i↑ n i↓ and applied it to the 1D Hubbard model, minimizing its energy variance as in the transcorrelated method [17][18][19]. Neuscamman et al. [20] proposed many-body Jastrow correlators, diagonal in the lattice basis, and truncated them to a subset of sites matching a given pattern; these authors compared projective solutions with those obtained stochastically via Monte Carlo.Here, we consider Hamiltonian transformations of the form e −J He J based on hermitian correlators J built from general two-body products of on-site operators over the entire lattice. The transformations here are generated by density (charge), spin, and Gutzwiller factor correlators, including density-spin crossed terms. Similar Jastrowtype correlators have been extensively discussed in the literature but almost always in a variational context [10]. Our transformed Hamiltonian is non-hermitian but can be solved in mean-field via projective equations similar in spirit to those of coupled cluster theory [20,21]. In this sense, the model is an extension that fits under the generalized coupled cluster label [22][23][24]. The fundamental difference is that traditional coupled cluster is formulated with particle-hole excitations out of a reference determinant via a non-hermitian cluster operator; the present model is constructed with on-site hermitian correlators.The main result of this paper is the realization that the Hausdorff series resulting from the non-unitary similarity transformation e −J He J can be analytically summed. This result follows from Lie algebraic arguments [25] after recognizing that bot...

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Variational ground states of the two-dimensional Hubbard model

Cited by 47 publications

References 65 publications

Equilibration and prethermalization in the Bose-Hubbard and Fermi-Hubbard models

Equilibration and prethermalization in the Bose-Hubbard and Fermi-Hubbard models

Density matrix embedding from broken symmetry lattice mean fields

Lie algebraic similarity transformed Hamiltonians for lattice model systems

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