We study the ground state phases of Bose-Fermi mixtures in one-dimensional optical lattices with quantum Monte Carlo simulations using the canonical worm algorithm. Depending on the filling of bosons and fermions, and the on-site intra-and interspecies interaction, different kinds of incompressible and superfluid phases appear. On the compressible side, correlations between bosons and fermions can lead to a distinctive behavior of the bosonic superfluid density and the fermionic stiffness, as well as of the equal-time Green functions, which allow one to identify regions where the two species exhibit anticorrelated flow. We present here complete phase diagrams for these systems at different fillings and as a function of the interaction parameters.

Studies of systems with two fermionic bands (or equivalently, layers) with repulsive interaction strength U have a long history, with the periodic Anderson model (PAM) being one of the most frequently considered Hamiltonians. In this paper, we use quantum Monte Carlo to study analogous issues for attractive interactions. As in the PAM, we focus on a case where one band (layer) is uncorrelated (U = 0), and the effect of hybridization V between the bands (layers) on the pairing correlations. A key difference with the PAM is that there is no sign problem, so that we are better able to explore the physics of doped bilayer attractive systems at low temperatures (except in the case of exponentially small transition temperatures) whereas ground state properties of repulsive models can be determined only at half-filling. For small V , pairing in the U < 0 layer induces pairing in the U = 0 layer. At larger V superfluidity 6

We investigate the magnetic properties of a heterostructure comprised of alternating metallic and Mott insulating layers of fermions with varying interlayer hybridization. Results from large-scale quantum Monte Carlo simulations at half-filling show clear evidence of induced magnetism in the metallic layers due to coupling to the Mott insulating layers at small to intermediate values of interlayer hopping. The in-plane magnetism is completely suppressed via a Kondo proximity effect when the coupling between adjacent layers is increased beyond a critical strength. The nature of the phase in the Kondo-like insulating regime is investigated and is shown to be dominated by simultaneous in-plane and interplane short-range correlations.

Experiments on cold atom systems in which a lattice potential is ramped up on a confined cloud have raised intriguing questions about how the temperature varies along isentropic curves, and how these curves intersect features in the phase diagram. In this paper, we study the isentropic curves of two models of magnetic phase transitions-the classical Blume-Capel Model (BCM) and the Fermi Hubbard Model (FHM). Both Mean Field Theory (MFT) and Monte Carlo (MC) methods are used. The isentropic curves of the BCM generally run parallel to the phase boundary in the Ising regime of low vacancy density, but intersect the phase boundary when the magnetic transition is mainly driven by a proliferation of vacancies. Adiabatic heating occurs in moving away from the phase boundary. The isentropes of the half-filled FHM have a relatively simple structure, running parallel to the temperature axis in the paramagnetic phase, and then curving upwards as the antiferromagnetic transition occurs. However, in the doped case, where two magnetic phase boundaries are crossed, the isentrope topology is considerably more complex.

In this paper we consider integers in base 10 like abc, where a, b, c are digits of the integer, such that abc 2 − (abc • cba) = ±n 2 , where n is a positive integer, as well as equations abc 2 −(abc•cba) = ±n 3 , and abc 3 −(abc•cba) = ±n 2 We consider asymptotic density of solutions. We also compare the results with ones with bases different from 10.