Supersolid structure and excitation spectrum of soft-core bosons in three dimensions

Ancilotto, Francesco; Rossi, Maurizio; Toigo, Flavio

doi:10.1103/physreva.88.033618

Cited by 36 publications

(35 citation statements)

References 36 publications

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“…The numerical simulation presented in Figure 11 shows the occurrence of crystallization for this model in 1D for a Lennard-Jones interaction. Similar results have been observed for the potential V (r) = 1 (0,1) (r) in higher dimensions [192,135,136,4,5,245,144,130,12].…”

Section: Quantum Modelssupporting

confidence: 76%

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The crystallization conjecture: a review

Blanc¹,

Lewin²

2015

EMS Surv. Math. Sci.

134

191

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In this article we describe the crystallization conjecture. It states that, in appropriate physical conditions, interacting particles always place themselves into periodic configurations, breaking thereby the natural translation-invariance of the system. This famous problem is still largely open. Mathematically, it amounts to studying the minima of a real-valued function defined on R 3N where N is the number of particles, which tends to infinity. We review the existing literature and mention several related open problems, of which many have not been thoroughly studied.

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Section: Quantum Modelssupporting

confidence: 76%

“…Since W has a positive Fourier transform, the same calculation as in (12) gives that the total interaction is bounded from below by…”

Section: Several Types Of Particlesmentioning

confidence: 96%

The crystallization conjecture: a review

Blanc¹,

Lewin²

2015

EMS Surv. Math. Sci.

134

191

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“…Quite interestingly, this repulsive interaction belongs to the class that has been recognized to induce cluster formation at high density in classical statistical mechanics [22,23], thanks to the relative freedom of particles at short distances. This has opened a recent flourishing of research on quantum cluster phases: in high dimensions, coexisting cluster crystal and superfluid order have been predicted, yielding supersolid behavior [11][12][13]24], while in one dimension (1D), cluster Luttinger liquids (CLL) have been proposed on a lattice [25,26].In this Letter, we investigate a prototypical system of N bosons in 1D at linear particle density n, governed by the following Hamiltonian in the continuum:where x i are the particle coordinates, r i j = |x i − x j | the distances, m is the mass and V 0 and R c are the strength and the radius of the soft-shoulder potential V(r). If not otherwise specified, in the following we use units of R c for the length, E c = 2 /mR 2 c for the energy, and /R c for the momenta (See Supplemental Material [27]).…”

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confidence: 99%

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confidence: 99%

Quantum Critical Behavior of One-Dimensional Soft Bosons in the Continuum

et al. 2017

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We consider a zero-temperature one-dimensional system of bosons interacting via the soft-shoulder potential in the continuum, typical of dressed Rydberg gases. We employ quantum Monte Carlo simulations, which allow for the exact calculation of imaginary-time correlations, and a stochastic analytic continuation method, to extract the dynamical structure factor. At finite densities, in the weakly-interacting homogeneous regime, a rotonic spectrum marks the tendency to clustering. With strong interactions, we indeed observe cluster liquid phases emerging, characterized by the spectrum of a composite harmonic chain. Luttinger theory has to be adapted by changing the reference lattice density field. In both the liquid and cluster liquid phases, we find convincing evidence of a secondary mode, which becomes gapless only at the transition. In that region, we also measure the central charge and observe its increase towards c = 3/2, as recently evaluated in a related extended Bose-Hubbard model, and we note a fast reduction of the Luttinger parameter. For 2-particle clusters, we then interpret such observations in terms of the compresence of a Luttinger liquid and a critical transverse Ising model, related to the instability of the reference lattice density field towards coalescence of sites, typical of potentials which are flat at short distances. Even in the absence of a true lattice, we are able to evaluate the spatial correlation function of a suitable pseudo-spin operator, which manifests ferromagnetic order in the cluster liquid phase, exponential decay in the liquid phase, and algebraic order at criticality.Quantum phase transitions (QPT) [1] play an intriguing role in many-body systems, due to the possibility of unveiling new exotic phases. The progress in the manipulation of ultracold gases allows for the exploration of QPTs, by engineering well-controlled synthetic quantum many-body systems, confined for example by optical lattices [2,3] or in quasi-onedimensional geometries [4][5][6][7]. Recently, Rydberg atoms [8] have emerged as a new route to QPTs [9,10]. These are atoms in highly-excited electronic states, with a very large electronic cloud. In particular, theoretical [11][12][13][14] and experimental [15][16][17] efforts have focused on ensembles of dressed Rydberg atoms, which are superpositions of the ground state and the above mentioned excited states, coupled via a Rabi process. Their effective interaction can be a soft-shoulder potential, with a flat repulsion up to a radius R c related to the highly excited state, and a repulsive van-der-Waals tail at large distances [11,12,[18][19][20][21]. Quite interestingly, this repulsive interaction belongs to the class that has been recognized to induce cluster formation at high density in classical statistical mechanics [22,23], thanks to the relative freedom of particles at short distances. This has opened a recent flourishing of research on quantum cluster phases: in high dimensions, coexisting cluster crystal and superfluid order have been predicted, yiel...

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“…The superfluid fraction could be extracted, for instance, from the calculated total momentum of the system under a Galilean boost, as obtained by solving the associated time-dependent equations of motion in the co-moving frame of reference (as done, for example, in Ref. 50 for a system of soft-core bosons). Since this is not the main subject of the present paper, I will not do this here.…”

Section: Iiib Inhomogeneous Systemmentioning

confidence: 99%

Kohn-Sham approach to Fermi gas superfluidity: The bilayer of fermionic polar molecules

Ancilotto

2016

Phys. Rev. A

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By using a well established 'ab initio' theoretical approach developed in the past to quantitatively study the superconductivity of condensed matter systems, based on the Kohn-Sham Density Functional theory, I study the superfluid properties and the BCS-BEC crossover of two parallel bi-dimensional layers of fermionic dipolar molecules, where the pairing mechanism leading to superfluidity is provided by the inter-layer coupling between dipoles. The finite temperature superfluid properties of both the homogeneous system and one were the fermions in each layer are confined by a square optical lattice are studied at half filling conditions, and for different values of the strength of the confining optical potential. The T=0 results for the homogeneous system are found to be in excellent agreement with Diffusion Monte Carlo results. The superfluid transition temperature in the BCS region is found to increase, for a given inter-layer coupling, with the strength of the confining optical potential. A transition occurs at sufficiently small interlayer distances, where the fermions becomes localized within the optical lattice sites in a square geometry with an increased effective lattice constant, forming a system of localized composite bosons. This transition should be signalled by a sudden drop in the superfluid fraction of the system.

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Supersolid structure and excitation spectrum of soft-core bosons in three dimensions

Cited by 36 publications

References 36 publications

The crystallization conjecture: a review

The crystallization conjecture: a review

Quantum Critical Behavior of One-Dimensional Soft Bosons in the Continuum

Kohn-Sham approach to Fermi gas superfluidity: The bilayer of fermionic polar molecules

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