**Физика Низких Температур: ***Том ***39**, Выпуск **9** (Сентябрь 2013), c. 1021-1030
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### Excitation spectrum in two-dimensional superfluid ^{4}He

**F. Arrigoni, E. Vitali, D.E. Galli, and L. Reatto**

Dipartimento di Fisica, Università degli Studi di Milano, 16 Celoria Via, Milano 20133, Italy

E-mail: Davide.Galli@unimi.it; davidemilio.galli@gmail.com

*Received March 14, 2013*

**Аннотация**

In this work we perform an *ab-initio* study of an ideal two-dimensional sample of ^{4}He atoms, a model for ^{4}He films adsorbed on several kinds of substrates. Starting from a realistic hamiltonian we face the microscopic study of the excitation phonon–roton spectrum of the system at zero temperature. Our approach relies on path integral
ground state Monte Carlo projection methods, allowing to evaluate exactly the dynamical density correlation
functions in imaginary time, and this gives access to the dynamical structure factor of the system *S*(*q*,w), containing
information about the excitation spectrum *E*(*q*), resulting in sharp peaks in *S*(*q*,w). The actual evaluation of *S*(*q*,w) requires the inversion of the Laplace transform in ill-posed conditions, which we face via the genetic inversion via falsification of theories technique. We explore the full density range from the region of spinodal decomposition to the freezing density, i.e., 0.0321 Å^{–2}
– 0.0658 Å^{–2}. In particular we follow the density dependence of the excitation spectrum, focusing on the low-wave vector behavior of *E*(*q*), the roton dispersion, the strength of single quasiparticle peak, *Z*(*q*), and the static density response function, c(*q*). As the density increases, the dispersion *E*(*q*) at low-wave vector changes from a superlinear (anomalous dispersion) trend to a sublinear (normal
dispersion) one, anticipating the crystallization of the system; at the same time the maxon–roton structure,
which is barely visible at low density, becomes well developed at high densities and the roton wave vector has a strong density dependence. Connection is made with recent inelastic neutron scattering results from highly ordered
silica nanopores partially filled with
^{4}He.

PACS: 67.25.bh Films and restricted geometries;

PACS: 67.25.dt Sound and excitations.

**Ключевые слова: **superfluidity, two-dimensional quantum fluids, elementary excitations, roton.