In this article we present a Monte Carlo calculation of the critical temperature and other thermodynamic quantities for the unitary Fermi gas with a population imbalance (unequal number of fermions in the two spin components). We describe an improved worm-type algorithm that is less prone to autocorrelations than the previously available methods and show how this algorithm can be applied to simulate the unitary Fermi gas in presence of a small imbalance. Our data indicate that the critical temperature remains almost constant for small imbalances h = µ/ε F < ≈ 0.2. We obtain the continuum result T c = 0.171(5)ε F in units of Fermi energy and derive a lower bound on the deviation of the critical temperature from the balanced limit,Using an additional assumption a tighter lower bound can be obtained. We also calculate the energy per particle and the chemical potential in the balanced and imbalanced cases.The Fermi-Hubbard model is the simplest lattice model for two-particle scattering. Its Hamiltonian in the grand canonical ensemble is given bywhere k = 1 m 3 j =1 (1 − cos k j ) is the discrete dispersion relation, and c † kσ (c kσ ) the time-dependent fermionic creation (annihilation) operator. We seth = k B = 1 throughout. We have chosen this simple dispersion relation for a better comparison with Ref.[4], where the same relation was used. It is possible to speed the approach to the continuum limit by choosing a more complex dispersion relation [10]. This will be explored in future work. This model describes nonrelativistic fermions of two species labeled by σ (which we call "spin up" and "spin down") with equal particle mass m. The attractive contact interaction is characterized by the coupling constant 1050-2947/2010/82(5)/053621 (11) 053621-1

We present controlled numerical results for the ground state spectral function of the resonant Fermi polaron in three dimensions. We establish the existence of a "dark continuum"-a region of anomalously low spectral weight between the narrow polaron peak and the rest of the spectral continuum. The dark continuum develops when the s-wave scattering length is of the order of the inverse Fermi wavevector, a 1/kF, i.e. in the absence of a small interaction-related parameter when the spectral weight is not expected to feature a near-perfect gap structure after the polaron peak.PACS numbers: 05.30. Fk, 05.10.Ln, 02.70.Ss Ultracold atomic fermions are a versatile and powerful tool to study quantum phenomena in many-body systems. Excellent experimental control and tunability of fermionic mixtures not only provide insight into the physics of such complex systems as electrons in materials or nuclear matter, but also enable a direct realization of fundamental quantum mechanical models. The key observation here is that short-range pairwise interactions near a broad Feshbach resonance [1] are universally characterized by a single dimensionless parameter k F a, where k F is the Fermi wavevector and a the s-wave scattering length, with k F a = ∞ corresponding to the so-called unitary limit.An important system realized in this way is the resonant Fermi polaron-a spin-down fermion (impurity) in a sea of spin-up fermions [2, 3] (here we consider three dimensions and equal mass m). As a limiting case, it is central for understanding the properties of strongly imbalanced Fermi mixtures. It is also the archetypal example of the dynamic impurity problem featuring strong renormalization of quasiparticle parameters, including changes of fundamental quantum numbers and statistics. At low temperature used in ultracold atom experiments the spinup subsystem can be regarded as non-interacting, while the impurity gets dressed with particle-hole excitations from the Fermi sea. For sufficiently strong interactions, k F a ≤ (k F a) c = 1.11(2) [4-8], a molecular bound state forms between the impurity and one spin-up fermion from the environment.Most theoretical studies of the Fermi polaron concentrate on computing its ground state energy E p , effective mass, and quasiparticle residue Z (modulus square of the overlap between the non-interacting and exact ground state wavefunctions) [4,5,[9][10][11][12][13][14][15][16]. Experiments, on the other hand, probe the spectral function using radiofrequency (rf) and photoemission spectroscopy [17][18][19][20]. The quantities of interest are then extracted from the measured spectrum; for instance, E p and Z are given by the frequency and spectral weight of the lowest-frequency sharp peak [17]. So far experiments have not yet resolved all the details of the polaron spectral function.Approximate calculations of the polaron spectral function [21][22][23][24], which lack control in the absence of a small parameter, report an interval of low spectral weight immediately after the polaron peak, if k F a 1. S...

We formulate the problem of numerical analytic continuation in a way that lets us draw meaningful conclusions about properties of the spectral function based solely on the input data. Apart from ensuring consistency with the input data (within their error bars) and the a priori and a posteriori (conditional) constraints, it is crucial to reliably characterize the accuracy-or even ambiguity-of the output. We explain how these challenges can be met with two approaches: stochastic optimization with consistent constraints and the modified maximum entropy method. We perform illustrative tests for spectra with a double-peak structure, where we critically examine which spectral properties are accessible (second peak position and its spectral weight) and which ones are lost (second peak width/shape). For an important practical example, we apply our protocol to the Fermi polaron problem.

We present results from Monte Carlo calculations investigating the properties of the homogeneous, spin-balanced unitary Fermi gas in three dimensions. The temperature is varied across the superfluid transition allowing us to determine the temperature dependence of the chemical potential, the energy per particle and the contact density. Numerical artifacts due to finite volume and discretization are systematically studied, estimated, and reduced.

We introduce and physically motivate the following problem in geometric combinatorics, originally inspired by analysing Bell inequalities. A grasshopper lands at a random point on a planar lawn of area 1. It then jumps once, a fixed distance , in a random direction. What shape should the lawn be to maximize the chance that the grasshopper remains on the lawn after jumping? We show that, perhaps surprisingly, a disc-shaped lawn is not optimal for any>0. We investigate further by introducing a spin model whose ground state corresponds to the solution of a discrete version of the grasshopper problem. Simulated annealing and parallel tempering searches are consistent with the hypothesis that, for <, the optimal lawn resembles a cogwheel with cogs, where the integer is close to [Formula: see text]. We find transitions to other shapes for [Formula: see text].