Extensive v2DM study of the one-dimensional Hubbard model for large lattice sizes: Exploiting translational invariance and parity

Verstichel, Brecht; Aggelen, Helen van; Poelmans, Ward; Wouters, Sebastian; Neck, Dimitri Van

doi:10.1016/j.comptc.2012.09.014

Cited by 14 publications

(29 citation statements)

References 46 publications

(71 reference statements)

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“…In this class are spin and charge-correlation functions commonly used to study lattice models. 24,25 To examine charge ordering, we utilize the standard charge correlation function ⟨̂̂⟩ + n n i i R (24) wherê =̂̂+̂α α β β † † n a a a a i i i i i (25) and express it as a function of the 2-RDM.…”

Section: Resultsmentioning

confidence: 99%

Strong Electron Correlation in Materials from Pair-Interacting Model Hamiltonians

Rubin

Mazziotti

2015

J. Phys. Chem. C

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Strong electron correlation in materials is explored within a class of model Hamiltonians that treat only pair interactions between electrons. The model is unique among typical spin Hamiltonians in that it does not have an effective mean-field reference wave function. The groundstate wave functions from all Hamiltonians in the model have the same oneelectron reduced density matrix (1-RDM); consequently, one-electron theories such as the Hartree−Fock and density functional theories are inapplicable. In contrast, the ground-state two-electron reduced density matrix (2-RDM) has a one-to-one mapping to the ground-state wave function. For a range of lattices including linear, ladder, and square topologies, we variationally compute the 2-RDM subject to constraints, known as Nrepresentability conditions, that are necessary for the 2-RDM to represent an N-electron ensemble density matrix. We find that for all model Hamiltonians the 2-RDM is accurately computed as long as the D, Q, and G N-representability conditions are supplemented with the T 2 condition. Energies, orbital and geminal occupation numbers, and correlation functions are computed. The model has applications to superconductivity as well as more general pairing phenomena in electronic systems. Effective methods are needed to treat strong electron correlation arising in the study of materials including the study of high-temperature superconductivity and phase transitions.

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Section: Resultsmentioning

confidence: 99%

Strong Electron Correlation in Materials from Pair-Interacting Model Hamiltonians

Rubin

Mazziotti

2015

J. Phys. Chem. C

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“…The constraint matrices A i in Eq. (19) contain the mappings among 2 D, 2 Q, and 2 G, the contractions to 1 D and 1 Q, and the fixed trace condition. Semidefinite programs for quantum chemical Hamiltonians have been solved with a variety of algorithms.…”

Section: B Semidefinite Programmingmentioning

confidence: 99%

Comparison of one-dimensional and quasi-one-dimensional Hubbard models from the variational two-electron reduced-density-matrix method

Rubin

Mazziotti

2014

Theor Chem Acc

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Minimizing the energy of an N -electron system as a functional of a two-electron reduced density matrix (2-RDM), constrained by necessary N -representability conditions (conditions for the 2-RDM to represent an ensemble N -electron quantum system), yields a rigorous lower bound to the groundstate energy in contrast to variational wavefunction methods. We characterize the performance of two sets of approximate constraints, (2,2)-positivity (DQG) and approximate (2,3)-positivity (DQGT) conditions, at capturing correlation in one-dimensional and quasi-one-dimensional (ladder) Hubbard models. We find that, while both the DQG and DQGT conditions capture both the weak and strong correlation limits, the more stringent DQGT conditions improve the ground-state energies, the natural occupation numbers, the pair correlation function, the effective hopping, and the connected (cumulant) part of the 2-RDM. We observe that the DQGT conditions are effective at capturing strong electron correlation effects in both one-and quasi-one-dimensional lattices for both half filling and less-than-half filling.

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“…One often finds continuously increasing singlet ground state energy for Hubbard models at increasing U on finite U domains in one [33][34][35] and two 36 dimensions as well, and even if we know that in 1D, the Bethe Ansatz E g result saturates at U → ∞, see Ref. 37 , we also know that often, the emergence of ferromagnetism at a fixed concentration is associated with the singlet E g increase in function of increasing U 38 .…”

Section: Properties Of the Deduced Ground Statementioning

confidence: 99%

Exact ground state for the four-electron problem in a 2D finite honeycomb lattice

Trencsényi

Глухов

Gulácsi

2014

Philosophical Magazine

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Working in a subspace with dimensionality much smaller than the dimension of the full Hilbert space, we deduce exact 4-particle ground states in 2D samples containing hexagonal repeat units and described by Hubbard type of models. The procedure identifies first a small subspace S in which the ground state |Ψ g is placed, than deduces |Ψ g by exact diagonalization in S. The small subspace is obtained by the repeated application of the HamiltonianĤ on a carefully chosen starting wave vector describing the most interacting particle configuration, and the wave vectors resulting from the application ofĤ, till the obtained system of equations closes in itself. The procedure which can be applied in principle at fixed but arbitrary system size and number of particles, is interesting by its own since provides exact information for the numerical approximation techniques which use a similar strategy, but apply non-complete basis for S. The diagonalization inside S provides an incomplete image about the low lying part of the excitation spectrum, but provides the exact |Ψ g . Once the exact ground state is obtained, its properties can be easily analyzed. The |Ψ g is found always as a singlet state whose energy, interestingly, saturates in the U → ∞ limit. The unapproximated results show that the emergence probabilities of different particle configurations in the ground state present "Zittern" (trembling) characteristics which are absent in 2D square Hubbard systems. Consequently, the manifestation of the local Coulomb repulsion in 2D square and honeycomb types of systems presents differences, which can be a real source in the differences in the many-body behavior.

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Extensive v2DM study of the one-dimensional Hubbard model for large lattice sizes: Exploiting translational invariance and parity

Cited by 14 publications

References 46 publications

Strong Electron Correlation in Materials from Pair-Interacting Model Hamiltonians

Strong Electron Correlation in Materials from Pair-Interacting Model Hamiltonians

Comparison of one-dimensional and quasi-one-dimensional Hubbard models from the variational two-electron reduced-density-matrix method

Exact ground state for the four-electron problem in a 2D finite honeycomb lattice

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