Backflow correlations in the Hubbard model: An efficient tool for the study of the metal-insulator transition and the large-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>U</mml:mi></mml:mrow></mml:math>limit

Tocchio, Luca F.; Becca, Federico; Gros, Claudius

doi:10.1103/physrevb.83.195138

Cited by 64 publications

(83 citation statements)

References 30 publications

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“…12 A major issue in the Hubbard model on the anisotropic triangular lattice is the possibility of stabilizing a spin-liquid phase (as seen in the experimental data). In addition, for generic values of the hopping parameters magnetic states with generic spiral order may be expected and indeed can be obtained within mean-field approaches, like for instance the Hartree-Fock (HF) approximation.…”

Section: B Effective Modelingmentioning

confidence: 99%

“…12,27 With this approximation, one finds that G ∝ lim q→0 q 2 N(q) , where N (q) = n −q n q and n q = 1/ √ L r,σ e iqr n r,σ . As such, the metallic phase is characterized by N (q)/q → const as q → 0, implying a vanishing gap at q = 0, and the insulating phase is characterized by N (q)/q → 0 as q → 0, implying a finite gap.…”

Section: A Modeling the Frontier Bandsmentioning

confidence: 99%

“…In this approach, each orbital that defines the unprojected states |BCS and |SP is taken to depend upon the many-body configuration, in order to incorporate virtual hopping processes. 12 All results presented here are obtained by fully incorporating the backflow corrections and optimizing individually every variational parameter in the mean-field BCS equation, in the Jastrow factors J c and J s , as well as in the backflow corrections.…”

Section: Paramagnetic Statesmentioning

confidence: 99%

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Importance of anisotropy in the spin-liquid candidate Me3EtSb[Pd(dmit)2]2

et al. 2013

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Organic charge-transfer salts based on the molecule Pd(dmit) 2 display strong electronic correlations and geometrical frustration, leading to spin-liquid, valence bond solid, and superconducting states, among other interesting phases. The low-energy electronic degrees of freedom of these materials are often described by a single band model: a triangular lattice with a molecular orbital representing a Pd(dmit) 2 dimer on each site. We use ab initio electronic structure calculations to construct and parametrize low-energy effective model Hamiltonians for a class of Me 4−n Et n X[Pd(dmit) 2 ] 2 (X = As, P, N, Sb) salts and investigate how best to model these systems by using variational Monte Carlo simulations. Our findings suggest that the prevailing model of these systems as a t − t triangular lattice is incomplete and that a fully anisotropic triangular lattice description produces importantly different results, including a significant lowering of the critical U of the spin-liquid phase.

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Section: B Effective Modelingmentioning

confidence: 99%

Section: A Modeling the Frontier Bandsmentioning

confidence: 99%

Section: Paramagnetic Statesmentioning

confidence: 99%

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Importance of anisotropy in the spin-liquid candidate Me3EtSb[Pd(dmit)2]2

et al. 2013

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“…Besides tensor networks, one can also include backflow correlations [38][39][40] to further improve the correlation effect of the variational wave function. The backflow correlations can be implemented in the pair-product wave function 40 , and in this case the additional computational cost of calculating kinetic energy arises because the pairing amplitude with backflow correlations is dependent on a real space configuration of electrons, which scales as O γN 2 s .…”

Section: B Variational Wave Function Ansatzmentioning

confidence: 99%

Variational Monte Carlo method for fermionic models combined with tensor networks and applications to the hole-doped two-dimensional Hubbard model

et al. 2017

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The conventional tensor-network states employ real-space product states as reference wave functions. Here, we propose a many-variable variational Monte Carlo (mVMC) method combined with tensor networks by taking advantages of both to study fermionic models. The variational wave function is composed of a pair product wave function operated by real space correlation factors and tensor networks. Moreover, we can apply quantum number projections, such as spin, momentum and lattice symmetry projections, to recover the symmetry of the wave function to further improve the accuracy. We benchmark our method for one-and two-dimensional Hubbard models, which show significant improvement over the results obtained individually either by mVMC or by tensor network. We have applied the present method to hole doped Hubbard model on the square lattice, which indicates the stripe charge/spin order coexisting with a weak d-wave superconducting order in the ground state for the doping concentration less than 0.3, where the stripe oscillation period gets longer with increasing hole concentration. The charge homogeneous and highly superconducting state also exists as a metastable excited state for the doping concentration less than 0.25.

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“…A size-consistent and efficient way to further improve the correlated state |Ψ for large on-site interactions is based on backflow correlations. In this approach, each orbital that defines the unprojected state |Φ 0 is taken to depend upon the many-body configuration, such to incorporate virtual hopping processes 46,47 . All results presented here are obtained by fully incorporating the backflow corrections and optimizing individually every variational parameter in H MF , in the Jastrow factor J , as well as for the backflow corrections 48 .…”

Section: Variational and Green's Function Monte Carlomentioning

confidence: 99%

Hidden Mott transition and large- U superconductivity in the two-dimensional Hubbard model

2016

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We consider the one-band Hubbard model on the square lattice by using variational and Green's function Monte Carlo methods, where the variational states contain Jastrow and backflow correlations on top of an uncorrelated wave function that includes BCS pairing and magnetic order. At half filling, where the ground state is antiferromagnetically ordered for any value of the on-site interaction U , we can identify a hidden critical point UMott, above which a finite BCS pairing is stabilized in the wave function. The existence of this point is reminiscent of the Mott transition in the paramagnetic sector and determines a separation between a Slater insulator (at small values of U ), where magnetism induces a potential energy gain, and a Mott insulator (at large values of U ), where magnetic correlations drive a kinetic energy gain. Most importantly, the existence of UMott has crucial consequences when doping the system: We observe a tendency to phase separation into a hole-rich and a hole-poor region only when doping the Slater insulator, while the system is uniform by doping the Mott insulator. Superconducting correlations are clearly observed above UMott, leading to the characteristic dome structure in doping. Furthermore, we show that the energy gain due to the presence of a finite BCS pairing above UMott shifts from the potential to the kinetic sector by increasing the value of the Coulomb repulsion.

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Backflow correlations in the Hubbard model: An efficient tool for the study of the metal-insulator transition and the large-Ulimit

Cited by 64 publications

References 30 publications

Importance of anisotropy in the spin-liquid candidate Me3EtSb[Pd(dmit)2]2

Importance of anisotropy in the spin-liquid candidate Me3EtSb[Pd(dmit)2]2

Variational Monte Carlo method for fermionic models combined with tensor networks and applications to the hole-doped two-dimensional Hubbard model

Hidden Mott transition and large- U superconductivity in the two-dimensional Hubbard model

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