Quantum Monte Carlo estimation of complex-time correlations for the study of the ground-state dynamic structure function

We present a method based on the Path Integral Monte Carlo formalism for the calculation of ground-state time correlation functions in quantum systems. The key point of the method is the consideration of time as a complex variable whose phase $\delta$ acts as an adjustable parameter. By using high-order approximations for the quantum propagator, it is possible to obtain Monte Carlo data all the way from purely imaginary time to $\delta$ values near the limit of real time. As a consequence, it is possible to infer accurately the spectral functions using simple inversion algorithms. We test this approach in the calculation of the dynamic structure function $S(q,\omega)$ of two one-dimensional model systems, harmonic and quartic oscillators, for which $S(q,\omega)$ can be exactly calculated. We notice a clear improvement in the calculation of the dynamic response with respect to the common approach based on the inverse Laplace transform of the imaginary-time correlation function.Comment: Accepted for publication on "Jornal of Chemical Physics

Optical lattices as a tool to study defect-induced superfluidity

We study the superfluid response, the energetic and structural properties of a one-dimensional ultracold Bose gas in an optical lattice of arbitrary strength. We use the Bose-Fermi mapping in the limit of infinitely large repulsive interaction and the diffusion Monte Carlo method in the case of finite interaction. For slightly incommensurate fillings we find a superfluid behavior which is discussed in terms of vacancies and interstitials. It is shown that both the excitation spectrum and static structure factor are different for the cases of microscopic and macroscopic fractions of defects. This system provides a extremely well-controlled model for studying defect-induced superfluidity.Comment: 14 pages, 13 figures, published versio

Weighted Contrastive Divergence

Learning algorithms for energy based Boltzmann architectures that rely on gradient descent are in general computationally prohibitive, typically due to the exponential number of terms involved in computing the partition function. In this way one has to resort to approximation schemes for the evaluation of the gradient. This is the case of Restricted Boltzmann Machines (RBM) and its learning algorithm Contrastive Divergence (CD). It is well-known that CD has a number of shortcomings, and its approximation to the gradient has several drawbacks. Overcoming these defects has been the basis of much research and new algorithms have been devised, such as persistent CD. In this manuscript we propose a new algorithm that we call Weighted CD (WCD), built from small modifications of the negative phase in standard CD. However small these modifications may be, experimental work reported in this paper suggest that WCD provides a significant improvement over standard CD and persistent CD at a small additional computational cost

Two-dimensional repulsive Fermi polarons with short and long-range interactions

We study the repulsive polaron problem in a two-component two-dimensional system of fermionic atoms. We use two different interaction models: a short-range (hard-disk) potential and a dipolar potential. In our approach, all the atoms have the same mass and we consider the system to be composed of a uniform bath of a single species and a single atomic impurity. We use the diffusion Monte Carlo method to evaluate polaron properties such as its chemical potential and pair distribution functions, together with a discussion on the deficit of volume induced by the impurity. We also evaluate observables that allow us to determine the validity of the quasi-particle picture: the quasi-particle residue and the effective mass of the polaron. Employing two different potentials allows us to identify the universality regime, where the properties depend only on the gas parameter $n a_s^2$ fixed by the bath density and the two-dimensional scattering length

Self-bound Bose mixtures

Recent experiments confirmed that fluctuations beyond the mean-field approximation can lead to self-bound liquid droplets of ultra-dilute binary Bose mixtures. We proceed beyond the beyond-mean-field approximation, and study liquid Bose mixtures using the variational hypernetted-chain Euler Lagrange method, which accounts for correlations non-perturbatively. Focusing on the case of a mixture of uniform density, as realized inside large saturated droplets, we study the conditions for stability against evaporation of one of the components (both chemical potentials need to be negative) and against liquid-gas phase separation (spinodal instability), the latter being accompanied by a vanishing speed of sound. Dilute Bose mixtures are stable only in a narrow range near an optimal ratio $\rho_1/\rho_2$ and near the total energy minimum. Deviations from a universal dependence on the s-wave scattering lengths are significant despite the low density.Comment: 5 pages, 5 figure

High-Momentum Response of Liquid 3He

A final-state-effects formalism suitable to analyze the high-momentum response of Fermi liquids is presented and used to study the dynamic structure function of liquid 3He. The theory, developed as a natural extension of the Gersch-Rodriguez formalism, incorporates the Fermi statistics explicitly through a new additive term which depends on the semidiagonal two-body density matrix. The use of a realistic momentum distribution, calculated using the diffusion Monte Carlo method, and the inclusion of this additive correction allows for good agreement with available deep-inelastic neutron scattering data