We compute the zero-temperature dynamical structure factor of one-dimensional liquid $^4$He by means of state-of-the-art Quantum Monte Carlo and analytic continuation techniques. By increasing the density, the dynamical structure factor reveals a tra
nsition from a highly compressible critical liquid to a quasi-solid regime. In the low-energy limit, the dynamical structure factor can be described by the quantum hydrodynamic Luttinger liquid theory, with a Luttinger parameter spanning all possible values by increasing the density. At higher energies, our approach provides quantitative results beyond the Luttinger liquid theory. In particular, as the density increases, the interplay between dimensionality and interaction makes the dynamical structure factor manifest a pseudo {it{particle-hole}} continuum typical of fermionic systems. At the low-energy boundary of such region and moderate densities, we find consistency, within statistical uncertainties, with predictions of a power-law structure by the recently-developed non-linear Luttinger liquid theory. In the quasi-solid regime we observe a novel behavior at intermediate momenta, which can be described by new analytical relations that we derive for the hard-rods model.
We present a fully detailed and highly performing implementation of the Linear Method [J. Toulouse and C. J. Umrigar (2007)] to optimize Jastrow-Feenberg and Backflow Correlations in many-body wave-functions, which are widely used in condensed matter
physics. We show that it is possible to implement such optimization scheme performing analytical derivatives of the wave-function with respect to the variational parameters achieving the best possible complexity O(N^3) in the number of particles N.
We study the momentum distributions of a three-dimensional resonant Bose-Fermi mixture in the molecular limit at zero temperature. For concentration of the bosons with respect to the fermions less or equal to one, each boson is bound to a fermion and
the system is composed of fermionic molecules plus excess fermions. Not only the bosonic condensate fraction goes to zero, signaling a quantum phase transition towards a normal phase, but a finite region of low momenta is depleted, depending on the concentration. This phenomenon is named indirect Pauli exclusion effect and is demonstrated via Fixed-Node Diffusion Monte Carlo simulations and T-matrix calculations.
We consider a Bose-Fermi mixture in the molecular limit of the attractive interaction between fermions and bosons. For a boson density smaller or equal to the fermion density, we show analytically how a T-matrix approach for the constituent bosons an
d fermions recovers the expected physical limit of a Fermi-Fermi mixture of molecules and atoms. In this limit, we derive simple expressions for the self-energies, the momentum distribution function, and the chemical potentials. By extending these equations to a trapped system, we determine how to tailor the experimental parameters of a Bose-Fermi mixture in order to enhance the indirect Pauli exclusion effect on the boson momentum distribution function. For the homogeneous system, we present finally a Diffusion Monte Carlo simulation which confirms the occurrence of such a peculiar effect.
We study a resonant Bose-Fermi mixture at zero temperature by using the fixed-node diffusion Monte Carlo method. We explore the system from weak to strong boson-fermion interaction, for different concentrations of the bosons relative to the fermion c
omponent. We focus on the case where the boson density $n_B$ is smaller than the fermion density $n_F$, for which a first-order quantum phase transition is found from a state with condensed bosons immersed in a Fermi sea, to a Fermi-Fermi mixture of composite fermions and unpaired fermions. We obtain the equation of state and the phase diagram, and we find that the region of phase separation shrinks to zero for vanishing $n_B$.
