Composite fermion-boson mapping for fermionic lattice models

Zhao, Jinmo; Jiménez-Hoyos, Carlos A.; Scuseria, Gustavo E.; Huerga, Daniel; Dukelsky, J.; Rombouts, Stefan; Ortíz, Gerardo

doi:10.1088/0953-8984/26/45/455601

Cited by 3 publications

(5 citation statements)

References 25 publications

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“…An attempt was performed in Ref. 5 to split the Fock space in each cluster according to its number parity: states with even (odd) parity where treated as bosonic (fermionic) degrees of freedom. An ansatz for the ground state was constructed in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Cluster-based mean-field and perturbative description of strongly correlated fermion systems: Application to the one- and two-dimensional Hubbard model

Jiménez-Hoyos

Scuseria

2015

Phys. Rev. B

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We introduce a mean-field and perturbative approach, based on clusters, to describe the ground state of fermionic strongly-correlated systems. In cluster mean-field, the ground state wavefunction is written as a simple tensor product over optimized cluster states. The optimization of the singleparticle basis where the cluster mean-field is expressed is crucial in order to obtain high-quality results. The mean-field nature of the ansatz allows us to formulate a perturbative approach to account for inter-cluster correlations; other traditional many-body strategies can be easily devised in terms of the cluster states. We present benchmark calculations on the half-filled 1D and (square) 2D Hubbard model, as well as the lightly-doped regime in 2D, using cluster mean-field and second-order perturbation theory. Our results indicate that, with sufficiently large clusters or to second-order in perturbation theory, a cluster-based approach can provide an accurate description of the Hubbard model in the considered regimes. Several avenues to improve upon the results presented in this work are discussed.

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Section: Introductionmentioning

confidence: 99%

“…An ansatz for the ground state was constructed in Ref. 5 as a tensor product of the bosonic and fermionic degrees of freedom; this decoupling, however, may not be justified in all cases and can potentially result in unphysical states.…”

Section: Introductionmentioning

confidence: 99%

Cluster-based mean-field and perturbative description of strongly correlated fermion systems: Application to the one- and two-dimensional Hubbard model

Jiménez-Hoyos

Scuseria

2015

Phys. Rev. B

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“…Lastly, regarding cPT4, we decided to compare the 2 × 2 with the 1 × 1 clusters for all the different methods, mainly for two reasons: (1) this comparison will shed some light on the difference between cPT2 and cCCSD mentioned in the previous paragraph, and (2) the cost of extrapolating cPT4 to the thermodynamic limit l → ∞ is prohibitive. Our results are summarized in Figure 8.…”

Section: Journal Of Chemical Theory and Computationmentioning

confidence: 99%

“…Unfortunately, despite tremendous effort and good progress, the accurate and efficient description of such systems is an open problem in quantum chemistry, because single-reference methods are generally inadequate. 1 Approaches based on composite particles (e.g., composite Fermion-boson mapping 2 ) have been proposed to tackle the multireference character inherent in these systems. In this work, which is a continuation of the work in ref 3, we discuss cluster mean-field (cMF) and correlated extensions based on perturbation theory (cPT) and coupled-cluster (cCC) for spin systems.…”

Section: Introductionmentioning

confidence: 99%

Coupled Cluster and Perturbation Theories Based on a Cluster Mean-Field Reference Applied to Strongly Correlated Spin Systems

Papastathopoulos-Katsaros

Hoyos

Henderson

et al. 2022

J. Chem. Theory Comput.

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We introduce perturbation and coupled-cluster theories based on a cluster mean-field reference for describing the ground state of strongly correlated spin systems. In cluster mean-field, the ground state wave function is written as a simple tensor product of optimized cluster states. The cluster language and the mean-field nature of the ansatz allow for a straightforward improvement which uses perturbation theory and coupled-cluster to account for intercluster correlations. We present benchmark calculations on the 1D chain and 2D square J 1–J 2 Heisenberg model, using cluster mean-field, perturbation theory, and coupled-cluster. We also present an extrapolation scheme that allows us to compute thermodynamic limit energies accurately. Our results indicate that, with sufficiently large clusters, the correlated methods (cPT2, cPT4, and cCCSD) can provide a relatively accurate description of the Heisenberg model in the regimes considered, which suggests that the methods presented can be used for other strongly correlated systems. Some ways to improve upon the methods presented in this work are discussed.

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“…In a realistic experimental system, the number of particles in each lattice site may break this con-straint. In addition, the ground-state phase diagrams of BH systems have been obtained by the analytical meanfield approach [38], the cell strong-coupling perturbation technique [39] and the composite boson mean-field theory [40,41] etc.…”

Section: Introductionmentioning

confidence: 99%

Cluster Gutzwiller study of the Bose-Hubbard ladder: Ground-state phase diagram and many-body Landau-Zener dynamics

et al. 2015

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We present a cluster Gutzwiller mean-field study for ground states and time-evolution dynamics in the Bose-Hubbard ladder (BHL), which can be realized by loading Bose atoms in double-well optical lattices. In our cluster mean-field approach, we treat each double-well unit of two lattice sites as a coherent whole for composing the cluster Gutzwiller ansatz, which may remain some residual correlations in each two-site unit. For a unbiased BHL, in addition to conventional superfluid phase and integer Mott insulator phases, we find that there are exotic fractional insulator phases if the inter-chain tunneling is much stronger than the intra-chain one. The fractional insulator phases can not be found by using a conventional mean-field treatment based upon the single-site Gutzwiller ansatz. For a biased BHL, we find there appear single-atom tunneling and interaction blockade if the system is dominated by the interplay between the on-site interaction and the inter-chain bias. In the many-body Landau-Zener process, in which the inter-chain bias is linearly swept from negative to positive or vice versa, our numerical results are qualitatively consistent with the experimental observation [Nat. Phys. 7, 61 (2011)]. Our cluster bosonic Gutzwiller treatment is of promising perspectives in exploring exotic quantum phases and time-evolution dynamics of bosonic particles in superlattices.

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Composite fermion-boson mapping for fermionic lattice models

Cited by 3 publications

References 25 publications

Cluster-based mean-field and perturbative description of strongly correlated fermion systems: Application to the one- and two-dimensional Hubbard model

Cluster-based mean-field and perturbative description of strongly correlated fermion systems: Application to the one- and two-dimensional Hubbard model

Coupled Cluster and Perturbation Theories Based on a Cluster Mean-Field Reference Applied to Strongly Correlated Spin Systems

Cluster Gutzwiller study of the Bose-Hubbard ladder: Ground-state phase diagram and many-body Landau-Zener dynamics

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