Weakly parametrized Jastrow ansatz for a strongly correlated Bose system

Lutsyshyn, Y.

doi:10.1063/1.4978707

Cited by 6 publications

(4 citation statements)

References 58 publications

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“…Although our work is devoted only to two interacting atoms, the solutions presented can be used as building-blocks for approximate methods dedicated to a larger number of particles. For example, similarly as it was done in different one-, [32][33][34] two-, 35,36 or three-dimensional, 37 one of the possible extensions is to use these two-particle solutions when variational ansatz of pair-correlated Jastrow wave functions are constructed. 38 Typically for this construction of the variational family, the corresponding two-body exact solution may serve as a prescription for trial wave functions.…”

Section: Discussionmentioning

confidence: 99%

Exactly solvable model of two interacting Rydberg-dressed atoms confined in a two-dimensional harmonic trap

Kościk

Sowiński

2019

Sci Rep

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Exactly solvable model of two Rydberg-dressed atoms moving in a quasi-two-dimensional harmonic trap is introduced and its properties are investigated. Depending on the strength of inter-particle interactions and the critical range of the potential, the two-particle eigenstates are classified with respect to the excitations of the center-of-mass motion, relative angular momentum, and relative distance variable. Having these solutions in hand, we discuss inter-particle correlations as functions of interaction parameters. We also present a straightforward prescription of how to generalize obtained solutions to higher dimensions.

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Section: Discussionmentioning

confidence: 99%

Exactly solvable model of two interacting Rydberg-dressed atoms confined in a two-dimensional harmonic trap

Kościk

Sowiński

2019

Sci Rep

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“…Although this correction improves the accuracy of the static structure factor at small wave vectors, contributions to the energy are small because the interatomic potential is not long-range. Further improvements based on parametrical expansions are also possible [63]. In other systems, it may be very well the case where higher-order and long-range correlations are important, which must be addressed case-by-case.…”

Section: Pair Product Approximationmentioning

confidence: 99%

Properties of fermionic systems with the path-integral ground state method

et al. 2023

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We investigate strongly correlated many-body systems composed of bosons and fermions with a fully quantum treatment using the path-integral ground state method, PIGS. To account for the Fermi-Dirac statistics, we implement the fixed-node approximation into PIGS, which we then call FN-PIGS. In great detail, we discuss the pair density matrices we use to construct the full density operator in coordinate representation, a vital ingredient of the method. We consider the harmonic oscillator as a proof-of-concept and, as a platform representing quantum many-body systems, we explore helium atoms. Pure ^44He systems demonstrate most of the features of the method. Complementarily, for pure ^33He, the fixed-node approximation resolves the ubiquitous sign problem stemming from anti-symmetric wave functions. Finally, we investigate ^33He-^44He mixtures, demonstrating the method’s robustness. One of the main features of FN-PIGS is its ability to estimate any property at temperature T = 0T=0 without any additional bias apart from the FN approximation; biases from long simulations are also excluded. In particular, we calculate the correlation function of pairs of equal and opposite spins and precise values of the ^33He kinetic energy in the mixture.

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“…In a many-body problem, the reduced mass m b used in Eq. ( 26) to generate the variational wave function can be treated as a variational parameter [61] which parameterizes different variational states. It was shown in Ref.…”

Section: Short-range Part Of Wave Functionmentioning

confidence: 99%

“…It was shown in Ref. [61] that by doing so one obtains a better accuracy for the description of liquid helium which is a strongly correlated system. In our case the correlations are not so strong and we find that keeping the two-body value, m b = m/2, is sufficient for performing calculations.…”

Section: Short-range Part Of Wave Functionmentioning

confidence: 99%

The Inverse-Square Interaction Phase Diagram: Unitarity in the Bosonic Ground State

et al. 2018

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Ground-state properties of bosons interacting via inverse square potential (three dimensional Calogero-Sutherland model) are analyzed. A number of quantities scale with the density and can be naturally expressed in units of the Fermi energy and Fermi momentum multiplied by a dimensionless constant (Bertsch parameter). Two analytical approaches are developed: the Bogoliubov theory for weak and the harmonic approximation (HA) for strong interactions. Diffusion Monte Carlo method is used to obtain the ground-state properties in a non-perturbative manner. We report the dependence of the Bertsch parameter on the interaction strength and construct a Padé approximant which fits the numerical data and reproduces correctly the asymptotic limits of weak and strong interactions. We find good agreement with beyond-mean field theory for the energy and the condensate fraction. The pair distribution function and the static structure factor are reported for a number of characteristic interactions. We demonstrate that the system experiences a gas-solid phase transition as a function of the dimensionless interaction strength. A peculiarity of the system is that by changing the density it is not possible to induce the phase transition. We show that the low-lying excitation spectrum contains plasmons in both phases, in agreement with the Bogoliubov and HA theories. Finally, we argue that this model can be interpreted as a realization of the unitary limit of a Bose system with the advantage that the system stays in the genuine ground state contrarily to the metastable state realized in experiments with short-range Bose gases.

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Weakly parametrized Jastrow ansatz for a strongly correlated Bose system

Cited by 6 publications

References 58 publications

Exactly solvable model of two interacting Rydberg-dressed atoms confined in a two-dimensional harmonic trap

Exactly solvable model of two interacting Rydberg-dressed atoms confined in a two-dimensional harmonic trap

Properties of fermionic systems with the path-integral ground state method

The Inverse-Square Interaction Phase Diagram: Unitarity in the Bosonic Ground State

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