Superstripes and quasicrystals in bosonic systems with hard-soft corona interactions

Abstract

The search for spontaneous pattern formation in equilibrium phases with genuine quantum properties is a leading direction of current research. In this paper, we investigate the effect of quantum fluctuations-zero-point motion and exchange interactions-on the phases of an ensemble of bosonic particles with isotropic hard-soft corona interactions. We perform extensive path-integral Monte Carlo simulations to determine their ground-state properties. A rich phase diagram, parametrized by the density of particles and the interaction strength of the soft-corona potential, reveals supersolid stripes, kagome, and triangular crystals in the low-density regime. In the high-density limit, we observe patterns with 12-fold rotational symmetry compatible with periodic approximants of quasicrystalline phases. We characterize these quantum phases by computing the superfluid density and the bond-orientational order parameter. Finally, we highlight the qualitative and quantitative differences of our findings with the classical equilibrium phases for the same parameter regimes.

Zonal estimators for quasiperiodic bosonic many-body phases

“…A prime example of a two-body model potential leading to quasiperiodic patterns is in the paradigmatic hard-soft corona potential, which is largely used to investigate purely classical systems [63]. The same model has also been applied to bosonic systems, where the effects of zero point motion, as well as quantum exchanges, disclose rich phase diagrams including quantum quasicrystal with 12-fold rotational symmetry [15]. Also, quantum properties of self-assembled cluster quasicrystals revealed that, in some cases, quantum fluctuations do not jeopardise dodecagonal structures, showing a small but finite local superfluidity [16].…”

“…Over the last thirty years, this has been amply demonstrated on quantum fluids [2,3] and, more recently, in ultra-cold gases like, for instance, dipolar systems [4][5][6][7][8] and Rydberg atoms [9][10][11]. For strongly-interacting quantum fluids, there is at present considerable interest towards the exploration of patterns owing peculiar symmetries such as quantum-cluster crystals [12,13], stripe phases [14,15], or cluster quasicrystals [16,17], with the aim of understanding fundamental physical phenomena. In this regard, also thanks to the increase in computational capabilities, advancements in PIMC methods continue to play a key role.…”

Properties of fermionic systems with the path-integral ground state method

“…Moreover, finally, for large imaginary times, this expression will approach the solution of a two-body Schrödinger equation (weighted by the corresponding energy eigenvalue), resulting in a many-body density matrix equivalent to a Jastrow-type wave function. These wave functions are well-known to accurately capture most ground state short-range correlations in systems that exhibit collective phenomena [30,33,34,58,59]. For systems composed of helium atoms, as stated by Leggett [60], the Jastrow function ansatz is the archetypal form of a variational ground state wave function.…”