More than 40 years ago, Andreev, Lifshitz and Chester suggested the possible existence of a peculiar solid phase of matter, the microscopic constituents of which can flow superfluidly without resistance due to the formation of zero-point defects in the ground state of self-assembled crystals. Yet, a physical system where this mechanism is unambiguously established remains to be found, both experimentally and theoretically. Here we investigate the zero-temperature phase diagram of two-dimensional bosons with finite-range soft-core interactions. For low particle densities, the system is shown to feature a solid phase in which zero-point vacancies emerge spontaneously and give rise to superfluid flow of particles through the crystal. This provides the first example of defect-induced, continuous-space supersolidity consistent with the Andreev–Lifshitz–Chester scenario. The peculiar supersolid phase of matter was predicted several decades ago, yet a physical system where it exists remains to be found. Cinti et al.investigate the zero-temperature phase diagram of bosons interacting by soft-core potentials and find that defects in it can give rise to a supersolid phase.
More than 40 years ago, Andreev, Lifshitz and Chester suggested the possible existence of a peculiar solid phase of matter, the microscopic constituents of which can flow superfluidly without resistance due to the formation of zero-point defects in the ground state of self-assembled crystals. Yet, a physical system where this mechanism is unambiguously established remains to be found, both experimentally and theoretically. Here we investigate the zero-temperature phase diagram of two-dimensional bosons with finite-range soft-core interactions. For low particle densities, the system is shown to feature a solid phase in which zero-point vacancies emerge spontaneously and give rise to superfluid flow of particles through the crystal. This provides the first example of defect-induced, continuous-space supersolidity consistent with the Andreev–Lifshitz–Chester scenario. The peculiar supersolid phase of matter was predicted several decades ago, yet a physical system where it exists remains to be found. Cinti et al.investigate the zero-temperature phase diagram of bosons interacting by soft-core potentials and find that defects in it can give rise to a supersolid phase.
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.
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.
Conclusive experimental evidence of a supersolid phase in any known condensed matter system is presently lacking. On the other hand, a supersolid phase has been recently predicted for a system of spinless bosons in continuous space, interacting via a broad class of soft-core, repulsive potentials. Such an interaction can be engineered in assemblies of ultracold atoms, providing a well-defined pathway to the unambiguous observation of this fascinating phase of matter. In this Letter, we study by first principles computer simulations the elementary excitation spectrum of the supersolid, and show that it features two distinct modes, namely, a solidlike phonon and a softer collective excitation, related to broken translation and gauge symmetry, respectively.
We study the low-temperature states of a system of spinless bosons trapped in a broad spherical shell. In our virtual (path-integral Monte Carlo) experiments, we specifically examine how the equilibrium structure and overall superfluidity of the system are affected by a change of the interparticle-potential core from hard to increasingly soft. In this manner we bridge the gap between the behaviors of two species of bosons: Helium-like atoms, which self-assemble into ordinary crystalline solids, and Rydberg-dressed atoms, which in simulation form cluster (super)solids. We also vary the particle mass, i.e., the quantumness of the system, so as to modify the relative stability of ``solid'' and fluid states. We thus find a whole spectrum of (finite-size) phases with a curved structure, including multilayer and cluster phases, as well as superfluids and single layer supersolids. In particular, we confirm that supersolids only occur in the presence of clusters. By considering three system sizes (from 60 to 180 particles), but rescaling the trap radius so that the density stays fixed, we verify that supersolid states only exist in the same range of particle masses. Our model serves as a platform to test how emergent properties are modified, in spherical geometry, in the crossover from atoms to dressed atoms.
Using an unbiased quantum Monte Carlo method, we obtain convincing evidence of the existence of a checkerboard supersolid at a commensurate filling factor 1/2 (a commensurate supersolid) in the soft-core Bose-Hubbard model with nearest-neighbor repulsions on a cubic lattice. In conventional cases, supersolids are realized at incommensurate filling factors by a doped-defect-condensation mechanism, where particles (holes) doped into a perfect crystal act as interstitials (vacancies) and delocalize in the crystal order. However, in the model, a supersolid state is stabilized even at the commensurate filling factor 1/2 without doping. By performing grand canonical simulations, we obtain a ground-state phase diagram that suggests the existence of a supersolid at a commensurate filling. To obtain direct evidence of the commensurate supersolid, we next perform simulations in canonical ensembles at a particle density ρ=1/2 and exclude the possibility of phase separation. From the obtained snapshots, we discuss its microscopic structure and observe that interstitial-vacancy pairs are unbound in the crystal order.
The properties of a macroscopic assembly of weakly repulsive bosons at zero temperature are well described by Gross-Pitaevskii mean-field theory. According to this formalism the system exhibits a quantum transition from superfluid to cluster supersolid as a function of pressure. We develop a thermodynamically rigorous treatment of the different phases of the system by adopting a variational formulation of the condensate wave function---represented as a sum of Gaussians---that is amenable to exact manipulations. Not only is this description quantitatively accurate, but it is also capable to predict the order (and sometimes even the location) of the transition. We consider a number of crystal structures in two and three dimensions and determine the phase diagram. Depending on the lattice, the transition from fluid to solid can be first order or continuous, a lower coordination entailing a milder transition. In two dimensions, crystallization would occur at the same pressure on three distinct lattices (square, honeycomb, and stripes), all providing metastable phases with respect to the triangular crystal. A similar scenario holds in three dimensions, where the simple-cubic and diamond crystals also share a common melting point; however, the stable crystal at low pressure is typically fcc. Upon compression and depending on the shape of the potential, the fcc crystal may transform into hcp. We conclude by sketching a theory of the solid-fluid interface and of quantum nucleation of the solid from the fluid.