Role of backflow correlations for the nonmagnetic phase of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>t</mml:mi><mml:mtext>–</mml:mtext><mml:msup><mml:mi>t</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:math>Hubbard model

Tocchio, Luca F.; Becca, Federico; Parola, Alberto; Sorella, Sandro

doi:10.1103/physrevb.78.041101

Cited by 98 publications

(121 citation statements)

References 26 publications

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“…For the one-body part |φ(t) , we employ the pair-product wave function. In addition, we include backflow correlations in the pair-product wave function for lattice model 29,42 . The time-dependent variational parameters are included in the correlation factors as well as in the one-body part with the backflow correlations.…”

Section: Time-dependent Variational Wave Functionmentioning

confidence: 99%

“…Recently, Tocchio et al proposed a way of introducing backflow correlations into a Slater determinant for lattice models and found that the backflow correlations substantially improve ground-state energy of frustrated electronic systems in the region above intermediate strength of coupling 29,42 . In a way similar to the approach by Tocchio et al, the backflow correlations for lattice models can be implemented in the pairproduct wave functions with the momentum projection as…”

Section: Backflow Correlationsmentioning

confidence: 99%

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Time-dependent many-variable variational Monte Carlo method for nonequilibrium strongly correlated electron systems

2015

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We develop a time-dependent variational Monte Carlo (t-VMC) method for quantum dynamics of strongly correlated electrons. The t-VMC method has been recently applied to bosonic systems and quantum spin systems. Here, we propose a time-dependent trial wave function with many variational parameters, which is suitable for nonequilibrium strongly correlated electron systems. As the trial state, we adopt the generalized pair-product wave function with correlation factors and quantum-number projections. This trial wave function has been proven to accurately describe ground states of strongly correlated electron systems. To show the accuracy and efficiency of our trial wave function in nonequilibrium states as well, we present our benchmark results for relaxation dynamics during and after interaction quench protocols of fermionic Hubbard models. We find that our trial wave function well reproduces the exact results for the time evolution of physical quantities such as energy, momentum distribution, spin structure factor, and superconducting correlations. These results show that the t-VMC with our trial wave function offers an efficient and accurate way to study challenging problems of nonequilibrium dynamics in strongly correlated electron systems.

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Section: Time-dependent Variational Wave Functionmentioning

confidence: 99%

Section: Backflow Correlationsmentioning

confidence: 99%

Time-dependent many-variable variational Monte Carlo method for nonequilibrium strongly correlated electron systems

2015

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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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Role of backflow correlations for the nonmagnetic phase of thet–t′Hubbard model

Cited by 98 publications

References 26 publications

Time-dependent many-variable variational Monte Carlo method for nonequilibrium strongly correlated electron systems

Time-dependent many-variable variational Monte Carlo method for nonequilibrium strongly correlated electron systems

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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