We investigate the properties of the superfluid phase in the three-dimensional disordered Bose-Hubbard model using quantum Monte Carlo simulations. The phase diagram is generated using Gaussian disorder on the onsite potential. Comparisons with box and speckle disorder show qualitative similarities leading to the reentrant behavior of the superfluid. Quantitative differences that arise are controlled by the specific shape of the disorder. Statistics pertaining to disorder distributions are studied for a range of interaction strengths and system sizes, where strong finite-size effects are observed. Despite this, both the superfluid fraction and compressibility remain self-averaging throughout the superfluid phase. Close to the superfluid-Bose-glass phase boundary, finite-size effects dominate but still suggest that self-averaging holds. Our results are pertinent to experiments with ultracold atomic gases where a systematic disorder averaging procedure is typically not possible.

The search for spontaneous pattern formation in equilibrium phases with genuine quantum properties is a leading direction of current research. In this paper, we investigate the effect of quantum fluctuations-zero-point motion and exchange interactions-on the phases of an ensemble of bosonic particles with isotropic hard-soft corona interactions. We perform extensive path-integral Monte Carlo simulations to determine their ground-state properties. A rich phase diagram, parametrized by the density of particles and the interaction strength of the soft-corona potential, reveals supersolid stripes, kagome, and triangular crystals in the low-density regime. In the high-density limit, we observe patterns with 12-fold rotational symmetry compatible with periodic approximants of quasicrystalline phases. We characterize these quantum phases by computing the superfluid density and the bond-orientational order parameter. Finally, we highlight the qualitative and quantitative differences of our findings with the classical equilibrium phases for the same parameter regimes.

The search for spontaneous pattern formation in equilibrium phases with genuine quantum properties is a leading direction of current research. In this work we investigate the effect of quantum fluctuations -zero point motion and exchange interactions -on the phases of an ensemble of bosonic particles with isotropic hard-soft corona interactions. We perform extensive path-integral Monte Carlo simulations to determine their ground state properties. A rich phase diagram, parametrized by the density of particles and the interaction strength of the soft-corona potential, reveals supersolid stripes, kagome and triangular crystals in the low-density regime. In the high-density limit we observe patterns with 12-fold rotational symmetry compatible with periodic approximants of quasicrystalline phases. We characterize these quantum phases by computing the superfluid density and the bond-orientational order parameter. Finally, we highlight the qualitative and quantitative differences of our findings with the classical equilibrium phases for the same parameter regimes.

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We investigate strongly correlated many-body systems composed of bosons and fermions with a fully quantum treatment using the path-integral ground state method, PIGS. To account for the Fermi-Dirac statistics, we implement the fixed-node approximation into PIGS, which we then call FN-PIGS. In great detail, we discuss the pair density matrices we use to construct the full density operator in coordinate representation, a vital ingredient of the method. We consider the harmonic oscillator as a proof-of-concept and, as a platform representing quantum many-body systems, we explore helium atoms. Pure ^44He systems demonstrate most of the features of the method. Complementarily, for pure ^33He, the fixed-node approximation resolves the ubiquitous sign problem stemming from anti-symmetric wave functions. Finally, we investigate ^33He-^44He mixtures, demonstrating the method’s robustness. One of the main features of FN-PIGS is its ability to estimate any property at temperature T = 0T=0 without any additional bias apart from the FN approximation; biases from long simulations are also excluded. In particular, we calculate the correlation function of pairs of equal and opposite spins and precise values of the ^33He kinetic energy in the mixture.