Temperature Dependence of the Vacancy Formation Energy in Solid 4^4He

We studied the thermal effects on the behavior of incommensurate solid $^4$He at low temperatures using the path integral Monte Carlo method. Below a certain temperature, depending on the density and the structure of the crystal, the vacancies delocalize and a finite condensate fraction appears. We calculated the vacancy formation energy as a function of the temperature and observed a behavior compatible with a two-step structure, with a gap of few K appearing at the onset temperature of off-diagonal long-range order. Estimation of the energy cost of creating two vacancies seems to indicate an effective attractive interaction among the vacancies but the large error inherent to its numerical estimation precludes a definitive statement.Comment: Contribution to the Special Issue on "Quantum Crystals": 9 pages, 3 figure

Simulating frustrated antiferromagnets with quadratically driven QED cavities

We propose a class of quantum simulators for antiferromagnetic spin systems, based on coupled photonic cavities in presence of two-photon driving and dissipation. By modeling the coupling between the different cavities through a hopping term with negative amplitude, we solve numerically the quantum master equation governing the dynamics of the open system and determine its non-equilibrium steady state. Under suitable conditions, the steady state can be described in terms of the degenerate ground states of an antiferromagnetic Ising model. When the geometry of the cavity array is incommensurate with the antiferromagnetic coupling, the steady state presents properties which bear full analogy with those typical of the spin liquid phases arising in frustrated magnets

On the robustness of strongly correlated multi-photon states in frustrated driven-dissipative cavity lattices

We present a theoretical study on the robustness of multi-photon states in a frustrated lattice of coupled nonlinear optical cavities, which are described by a driven-dissipative Bose-Hubbard model. In particular, we focus here on a Lieb lattice with two elementary cells and periodic boundary conditions. Due to the geometric frustration of the lattice, the non-equilibrium steady state can exhibit dark sites with low photon density and strong correlations, ascribable to the population of multi-photon modes. We explore the sensitivity of such strong correlations on the random inhomogeneity of the lattice parameters. We show that the correlations are more sensitive to the inhomogeneity of the cavity frequencies than to the random fluctuations of the hopping strength.Comment: Accepted for publication on EPJ-Special Topics "Quantum gases and quantum coherence": 10 pages, 5 figure

Path Integral Monte Carlo and Bose-Einstein condensation in quantum fluids and solids

Several microscopic theories point out that Bose-Einstein condensation (BEC), i.e., a macroscopic occupation of the lowest energy single particle state in many-boson systems, may appear also in quantum fluids and solids and that it is at the origin of the phenomenon of superfluidity. Nevertheless, the connection between BEC and superfluidity is still matter of debate, since the experimental evidences indicating a non zero condensate fraction in superfluid helium are only indirect. In the theoretical study of BEC in quantum fluids and solids, perturbative approaches are useless because of the strong correlations between the atoms, arising both from the interatomic potential and from the quantum nature of the system. Microscopic Quantum Monte Carlo simulations provide a reliable description of these systems. In particular, the Path Integral Monte Carlo (PIMC) method is very suitable for this purpose. This method is able to provide exact results for the properties of the quantum system, both at zero and finite temperature, only with the definition of the Hamiltonian and of the symmetry properties of the system, giving an easy picture for superfluidity and BEC in many-boson systems. In this thesis, we apply PIMC methods to the study of several quantum fluids and solids. We describe in detail all the features of PIMC, from the sampling methods to the estimators of the physical properties. We present also the most recent techniques, such as the high-order approximations for the thermal density matrix and the worm algorithm, used in PIMC to provide reliable simulations. We study the liquid phase of condensed 4He, providing unbiased estimations of the one-body density matrix g1(r). We analyze the model for g1(r) used to fit the experimental data, highlighting its merits and its faults. In particular we see that, even if it presents some difficulties in the description of the overall behavior of g1(r), it can provide an accurate estimation of the kinetic energy K and of the condensate fraction n0 of the system. Furthermore, we show that our results for n0 as a function of the pressure are in a good agreement with the most recent experimental results. The study of the solid phase of 4He is the most significant part of this thesis. The recent observation of non classical rotational inertia (NCRI) effects in solid helium has generated big interest in the study of an eventual supersolid phase, characterized at the same time by crystalline order and superfluidity. Nevertheless, until now it has been impossible to give a theoretical model able to describe all the experimental evidences. In this work, we perform PIMC simulations of 4He at high densities, according to different microscopic configurations of the atoms. In commensurate crystals we see that BEC does not appear, our model being able to reproduce the momentum distribution obtained form neutron scattering experiments. In a crystal with vacancies, we have been able to see a transition to a superfluid phase at temperatures in agreement with experimental results if the vacancy concentration is low enough. In amorphous solids, superfluid effects are enhanced but appear at temperatures higher than the experimental estimation for the transition temperature. Finally, we study also metastable disordered configurations in molecular para-hydrogen at low temperature. The aim of this study is to investigate if a Bose liquid other than helium can display superfluidity. Choosing accurately a ¿quantum liquid¿ initial configuration and the dimensions of the simulation box, we have been able to frustrate the formation of the crystal and to calculate the temperature dependence of the superfluid density, showing a transition to a superfluid phase at temperatures close to 1 K

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

Dynamical properties of dissipative XYZ Heisenberg lattices

We study dynamical properties of dissipative XYZ Heisenberg lattices where anisotropic spin-spin coupling competes with local incoherent spin flip processes. In particular, we explore a region of the parameter space where dissipative magnetic phase transitions for the steady state have been recently predicted by mean-field theories and exact numerical methods. We investigate the asymptotic decay rate towards the steady state both in 1D (up to the thermodynamical limit) and in finite-size 2D lattices, showing that critical dynamics does not occur in 1D, but it can emerge in 2D. We also analyze the behavior of individual homodyne quantum trajectories, which well reveal the nature of the transition