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arXiv:1603.07270 · Physical review. B./Physical review. B

Ground-state phase diagram of Gaussian-core bosons in two dimensions

Peter Kroiß, Massimo Boninsegni, Lode Pollet

Published May 31, 2016• 7 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.93.174520

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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.
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 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.
We study the ground-state properties of repulsively interacting bosons on the honeycomb lattice using large-scale quantum Monte Carlo simulations. In the hard-core limit, the half-filled system develops long-ranged diagonal order for sufficiently strong nearest-neighbor repulsion. This staggered solid melts at a first-order quantum phase transition into the superfluid phase, without the presence of any intermediate supersolid phase. Within the superfluid phase, both the superfluid density and the compressibility exhibit local minima near the particle (hole) density of one quarter, while the density and the condensate fraction show inflection points in this region. Relaxing the hard-core constraint, supersolid phases emerge for soft-core bosons. The suppression of the superfluid density is found to persist for sufficiently large, finite on-site repulsion.
The ground-state phase properties of a two-dimensional Bose system with dipole-dipole interactions is studied by means of quantum Monte Carlo techniques. Limitations of mean-field theory in a two-dimensional geometry are discussed. A quantum phase transition from gas to solid is found. Crystal is tested for existence of a supersolid in the vicinity of the phase transition. Existence of mesoscopic analogue of the off-diagonal long-range order is shown in the one-body density matrix in a finite-size crystal. Non-zero superfluid fraction is found in a finite-size crystal, the signal being dramatically increased in presence of vacancies.
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 determine the finite-temperature phase diagram of the square lattice hard-core boson Hubbard model with nearest neighbor repulsion using quantum Monte Carlo simulations. This model is equivalent to an anisotropic spin-1/2 XXZ model in a magnetic field. We present the rich phase diagram with a first order transition between a solid and superfluid phase, instead of a previously conjectured supersolid and a tricritical end point to phase separation. Unusual reentrant behavior with ordering upon increasing the temperature is found, similar to the Pomeranchuk effect in 3He.