In two-dimensional bosonic systems ultrasoft interactions develop an interesting phenomenology that ultimately leads to the appearance of supersolid phases in free space conditions. While suggested in early theoretical works and despite many further analytical efforts, the appearance of these exotic phases as well as the detailed shape of the ground-state phase diagrams have not been established yet. Here we develop a variational mean-field calculation for a generic quantum system with cluster-forming interactions. We show that by including the restriction of a fixed integer number of particles per cluster the ground-state phase diagram can be obtained in great detail. The great detail includes the determination of coexistence regimes of crystals of different occupancy as well as crystals with superfluid phases. To illustrate the application of the method we consider the softened van der Waals potential, for which the phase diagram is known via quantum Monte Carlo simulations. For densities other than that corresponding to the single-particle crystal, our results show very good quantitative agreement with the simulations regarding the location of the superfluid transitions. Additionally, the phase diagrams suggest that the solid-superfluid coexistence could be a reliable marker to locate supersolidity.
In two-dimensional bosonic systems ultrasoft interactions develop an interesting phenomenology that ultimately leads to the appearance of supersolid phases in free space conditions. While suggested in early theoretical works and despite many further analytical efforts, the appearance of these exotic phases as well as the detailed shape of the ground-state phase diagrams have not been established yet. Here we develop a variational mean-field calculation for a generic quantum system with cluster-forming interactions. We show that by including the restriction of a fixed integer number of particles per cluster the ground-state phase diagram can be obtained in great detail. The great detail includes the determination of coexistence regimes of crystals of different occupancy as well as crystals with superfluid phases. To illustrate the application of the method we consider the softened van der Waals potential, for which the phase diagram is known via quantum Monte Carlo simulations. For densities other than that corresponding to the single-particle crystal, our results show very good quantitative agreement with the simulations regarding the location of the superfluid transitions. Additionally, the phase diagrams suggest that the solid-superfluid coexistence could be a reliable marker to locate supersolidity.
The ground state of a two-dimensional (2D) system of Bose particles of spin zero, interacting via a repulsive Gaussian-core potential, has been investigated by means of quantum Monte Carlo simulations. The quantum phase diagram is qualitatively identical to that of 2D Yukawa bosons. While the system is a fluid at all densities for weak coupling, in the strong-coupling regime it transitions upon compression from a low-density superfluid to a crystal, and then into a reentrant superfluid phase. No evidence of a (supersolid) cluster crystal phase is seen.
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 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.
We investigate the properties of strongly interacting bosons in two dimensions at zero temperature using mean-field theory, a variational ansatz for the ground-state wave function, and Monte Carlo methods. With on-site and short-range interactions a rich phase diagram is obtained. Apart from the homogeneous superfluid and Mott-insulating phases, inhomogeneous charge-density wave phases appear, that are stabilized by the finite-range interaction. Furthermore, our analysis demonstrates the existence of a supersolid phase, in which both long-range order (related to the charge-density wave) and off-diagonal long-range order coexist. We also obtain the critical exponents for the various phase transitions.
We study the emergence of quasicrystal configurations in the ground-state phase diagram of bosonic systems interacting through pair potentials of Lifshitz's type. By using a variational mean-field approach, we determine the relevant features of the corresponding potential interaction kind stabilizing such quasicrystalline states in two dimensions. Unlike their classical counterpart, in which the interplay between only two wave vectors determines the resulting symmetries of the solutions, the quantum picture relates in a more complex way to the instabilities of the excitation spectrum. Moreover, the quantum quasicrystal patterns are found to emerge as the ground state with no need of moderate thermal fluctuations. The study extends to the exploration of the excitation properties and the possible existence of superquasicrystals, i.e., supersolidlike quasicrystalline states in which the long-range nonperiodic density profile coexists with a nonzero superfluid fraction. Our calculations suggest that, in an intermediate region between the homogeneous superfluid and the normal quasicrystal phases, these exotic states indeed exist at zero temperature. Comparison with full numerical simulations provides a solid verification of the variational approach adopted in this paper.
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.