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Crystals 2018, 8(6), 246; https://doi.org/10.3390/cryst8060246

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

1
Departament de Física, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain
2
Institute of Spectroscopy (Russian Academy of Sciences), 108840 Troitsk, Moscow, Russia
3
National Research University Higher School of Economics, 109028 Moscow, Russia
*
Author to whom correspondence should be addressed.
Received: 22 April 2018 / Revised: 4 June 2018 / Accepted: 4 June 2018 / Published: 8 June 2018
(This article belongs to the Special Issue Quantum Crystals)
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Abstract

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. View Full-Text
Keywords: unitarity; gas-solid phase transition; plasmons; Bogoliubov theory; harmonic approximation theory; diffusion Monte Carlo method unitarity; gas-solid phase transition; plasmons; Bogoliubov theory; harmonic approximation theory; diffusion Monte Carlo method
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Astrakharchik, G.E.; Kryuchkov, P.S.; Kurbakov, I.L.; Lozovik, Y.E. The Inverse-Square Interaction Phase Diagram: Unitarity in the Bosonic Ground State. Crystals 2018, 8, 246.

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