Abstract
We analyze the many-body phases of an ensemble of particles interacting via a Lifshitz–Petrich–Gaussian pair potential in a harmonic confinement. We focus on specific parameter regimes where we expect decagonal quasiperiodic cluster arrangements. Performing classical Monte Carlo as well as path integral quantum Monte Carlo methods, we numerically simulate systems of a few thousand particles including thermal and quantum fluctuations. Our findings indicate that the competition between the intrinsic length scale of the harmonic oscillator and the wavelengths associated to the minima of the pair potential generically lead to a destruction of the quasicrystalline pattern. Extensions of this work are also discussed.
Highlights
Quasicrystals are quasiperiodic systems which break translational symmetry and display long-range order without being periodic [1]
A microscopic mechanism to generate a host of different phases including quasicrystals is based on simultaneous instability at more than one length scale, corresponding to degenerate minima of the Fourier transform of the potential [3,4]
Regarding the quantum counterpart (λ > 0), we investigated the equilibrium properties of the system described by the Hamiltonian (1) employing first-principle computer simulations based on a continuous-space path integral Monte Carlo [35,36]
Summary
Quasicrystals are quasiperiodic systems which break translational symmetry and display long-range order without being periodic [1]. It is important to note that power-law interactions are singular at the origin, prohibiting the approach of two or more particles at very small interparticle distances, as in the case of dipolar potentials [6,7] To circumvent this effect, one may engineer different types of interactions which are finite for small separations. We focus on a restricted parameter regime where we expect a decagonal quasiperiodic arrangement of clusters in free space, and study the effect on the many-body phases, adding a trapping potential. To explore such phases, we employ either classical Monte Carlo simulations to analyze the effect of thermal fluctuations or path integral quantum Monte Carlo methods for the investigation of quantum fluctuations.
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