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arXiv:1205.2126 · Physical Review B

Mean-field and stability analyses of two-dimensional flowing soft-core bosons modeling a supersolid

Masaya Kunimi, Yusuke S. Kato

Published Aug 24, 2012• 67 citations
arXivHTMLPDF

Abstract

The soft-core boson system is one of the simplest models of supersolids, which have both off-diagonal long-range order (Bose--Einstein condensation) and diagonal long-range order (crystalline order). Although this model has been studied from various points of view, studies of the stability of current-flowing states are lacking. Solving the Gross--Pitaevskii and Bogoliubov equations, we obtain excitation spectra in superfluid, supersolid, and stripe phases. On the basis of the results of the excitation spectra, we present a stability phase diagram that shows the region of the metastable superflow states for each phase.

DOI
10.1103/physrevb.86.060510

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The soft-core boson system is one of the simplest models of supersolids, which have both off-diagonal long-range order (Bose--Einstein condensation) and diagonal long-range order (crystalline order). Although this model has been studied from various points of view, studies of the stability of current-flowing states are lacking. Solving the Gross--Pitaevskii and Bogoliubov equations, we obtain excitation spectra in superfluid, supersolid, and stripe phases. On the basis of the results of the excitation spectra, we present a stability phase diagram that shows the region of the metastable superflow states for each phase.
We investigate the zero-temperature excitation spectrum of two-dimensional soft-core bosons for a wide range of parameters and across the phase transition from a superfluid to a supersolid state. Based on mean-field calculations and recent quantum Monte Carlo results, we demonstrate the applicability of the Bogoliubov-de Gennes equations, even at high interaction strengths where the system forms an insulating cluster crystal. Interestingly, our study reveals that the maximum energy of the longitudinal phonon band in the supersolid phase connects to the maxon energy of the superfluid at the phase transition.
Abstract We investigate the superfluid fraction of crystalline stationary states within the framework of mean-field Gross–Pitaevskii theory. Our primary focus is on a two-dimensional Bose–Einstein condensate with a non-local soft-core interaction, where the superfluid fraction is described by a rank-2 tensor. We then calculate the superfluid fraction tensor for crystalline states exhibiting triangular, square, and stripe geometries across a broad range of interaction parameters. Factors leading to an anisotropic superfluid fraction tensor are also considered. We also refine the Leggett bounds for the superfluid fraction of the 2D system. We systematically compare these bounds to our full numerical results, and other results in the literature. This work is of direct relevance to other supersolid systems of current interest, such as supersolids produced using dipolar Bose–Einstein condensates.
We study quantum phase transitions in the ground state of the two dimensional hard-core boson Hubbard Hamiltonian. Recent work on this and related models has suggested "supersolid" phases with simultaneous diagonal and off-diagonal long range order. We show numerically that, contrary to the generally held belief, the most commonly discussed "checkerboard" supersolid is thermodynamically unstable. Furthermore, this supersolid cannot be stabilized by next-near-neighbor interaction. We obtain the correct phase diagram using the Maxwell construction. We demonstrate that the "striped" supersolid is thermodynamically stable and is separated from the superfluid phase by a continuous phase transition.
The supersolid phase of soft-core bosons in two dimensions is investigated using the self-consistent Hartree-Fock and quantum Monte Carlo methods. An approximate phase diagram at finite temperatures is initially constructed using the mean-field approach, which is subsequently validated through precise path-integral simulations, enabling a microscopic characterization of the various phases. Superfluid and melting/freezing transitions are analyzed through the superfluid density and the long-range behavior of correlation functions associated with positional and orientational order, in accordance with the general picture of Berezinskii-Kosterlitz-Thouless transitions. A broad region at low temperatures is identified where the supersolid phase exists, separating the uniform superfluid phase from the normal quasicrystal phase. Additionally, a potential intermediate hexatic phase with quasi-long-range orientational order is identified in a narrow region between the normal solid and fluid phases. These findings establish self-consistent Hartree-Fock theory beyond the local density approximation as an effective tool, complementary to computationally intensive quantum Monte Carlo simulations, for investigating the melting of the supersolid phase and the possible emergence of the hexatic superfluid phase in bosonic systems with various interaction potentials.
The low temperature phase diagram of an assembly of Bose particles, interacting via a simple soft disc potential, is studied numerically by means of Monte Carlo simulations. At sufficiently high densities, the system features a cluster crystal phase, as observed in its classical counterpart. In the low temperature limit, and in a relatively wide region of parameter space, the quantum cluster crystal undergoes a transition to a supersolid phase, displaying both a finite superfluid fraction and crystalline order. We argue that soft-core Bosons ought be regarded as a ‘minimal model’ of continuous-space supersolidity. With the aim of elucidating the interplay between superfluid response and solid order, we compute the excitation spectrum of the system. A comparison of that of the insulating cluster crystal with that of the supersolid, shows that the latter features an additional acoustic mode.
Supersolid is a special state of matter with both superfluid properties and spontaneous modulation of particle density. In this paper we focus on the supersolid stripe phase realized in a spin-orbit-coupled Bose-Einstein condensate and explore the properties of a class of metastable supersolids. In particular, we study a one-dimensional supersolid whose characteristic wave number kkk (magnitude of wave vector) deviates from km{k}_{m}km​, i.e., the one in the ground state. In other words, the period of density modulation is shorter or longer than the one in the ground state. We find that this class of supersolids can still be stable if their wave numbers fall in the range kc1<k<kc2{k}_{c1}<k<{k}_{c2}kc1​<k<kc2​, with two thresholds kc1{k}_{c1}kc1​ and kc2{k}_{c2}kc2​. Stripes with kkk outside this range suffer from dynamical instability with a complex Bogoliubov excitation spectrum at long wavelength. Experimentally, these stripes with kkk different from km{k}_{m}km​ are accessible by exciting the longitudinal spin dipole mode, resulting in temporal oscillation of the stripe period as well as kkk. Within the mean-field Gross-Pitaevskii theory, we numerically confirm that for a large enough amplitude of spin dipole oscillation, the stripe states become unstable through breaking periodicity, in qualitative agreement with the existence of thresholds of kkk for stable stripes. Our work extends the concept of supersolid and uncovers an unconventional class of metastable supersolids to explore.