Quantum Monte Carlo study of the dynamic structure factor in the gas and crystal phase of hard-sphere bosons

Abstract

We investigate the dynamic structure factor of a system of Bose particles at zero temperature using quantum Monte Carlo methods. Interactions are modeled using a hard-sphere potential of size a and simulations are performed for values of the gas parameter na 3 ranging from the dilute regime up to densities n where the thermodynamically stable phase is a solid. With increasing density, we observe a crossover of the dispersion of elementary excitations from a Bogoliubov-type spectrum to a phonon-maxon-roton curve and the emergence of a broad multiphonon contribution accompanying the single-quasiparticle peak. In particular, for na 3 = 0.2138, which corresponds to superfluid 4 He at equilibrium density, the extracted spectrum turns out to be in good agreement with the experimental energy-momentum dispersion relation in the roton region and for higher momenta. The behavior of the spectral function at the same density in the stable solid and metastable gas phase above the freezing point is also discussed.

Roton Excitations and the Fluid–Solid Phase Transition in Superfluid 2D Yukawa Bosons

“…The He-He interaction is characterized by a hard repulsive core at short distance and by a rather weak attraction at larger distances, as typified by the Lennard-Jones form. In fact, it is well-established that most properties of such system are determined by the hard core, the attractive tail playing a minor role [8][9][10].…”

“…The situation is different for systems at large density, in which case V (r) explicitly enters into the microscopic description of the system. A number of model interactions have been studied by many-body theories and simulations [4,[6][7][8]. The He-He interaction is characterized by a hard repulsive core at short distance and by a rather weak attraction at larger distances, as typified by the Lennard-Jones form.…”

“…This important property makes the dynamical structure factor a quantity of paramount importance in the experimental and theoretical investigation of many-body quantum systems, ranging from superfluid and solid 4 He [18][19][20][21][22][23] to ultracold atomic gases [8,24]. For strongly-interacting systems, the quantitative study of the dynamical structure factor must typically be supported by numerical calculations or simulations.…”

“…The first application of quantum Monte Carlo (QMC) methods to the calculation of the dynamical structure factor dates back to [25][26][27] for lattice systems and [28] for homogeneous systems. Further developments have made possible the calculation of S(q, ω) in systems of 4 He atoms [20,23], as well as in two-dimensional (2D) homogeneous electron gases and systems of 3 He atoms [29][30][31], and systems of Bose hard spheres [8,10].…”

“…In the present work, we compute the dynamical structure factor of a zero-temperature system of 2D-SC Bosons, using the shadow path integral ground state method (SPIGS) [36,37] to compute the imaginary-time intermediate scattering function, F (q, τ ) (see equation (6)), and a genetic algorithm, known as genetic inversion via falsification of theories (GIFT) [8,20], to retrieve S(q, ω) from F (q, τ ).…”