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Correlated density matrix theory is generalized to investigate equilibrium properties of normal Fermi Liquids such as 3He and nuclear matter at nonzero temperatures. The results also generalize the Fermi-hypernetted-chain technique that is…
The variational determination of the two-fermion reduced density matrix is described for harmonically trapped, ultracold few-fermion systems in one dimension with equal spin populations. This is accomplished by formulating the problem as a…
Fermi gases with magnetically tunable interactions provide a clean and controllable laboratory system for modeling interparticle interactions between fermions in nature. The s-wave scattering length, which is dominant a low temperature, is…
We consider interacting Fermi systems close to the unitary regime and compute the corrections to the energy density that are due to a large scattering length and a small effective range. Our approach exploits the universality of the density…
In this chapter we review recent experimental and theoretical work on various novel superfluid phases in fermion systems, that result from pairing fermions of different species with unequal densities. After briefly reviewing existing…
In a recent paper we have suggested that the finite temperature density matrix can be computed efficiently by a combination of polynomial expansion and iterative inversion techniques. We present here significant improvements over this…
Properties of confined mesoscopic systems have been extensively studied numerically over recent years. We discuss an analytical approach to the study of finite rotating fermionic systems in two dimension. We first construct the energy…
A rational expansion of the Fermi density operator is proposed. This approach allows to calculate efficiently physical properties of fermionic systems at finite temperatures without solving an eigenvalue problem. Using N evaluations of the…
Some algorithms for the numerically exact treatment of fermion determinants are summarised. This is not supposed to be a review, rather a concise handbook. The audience is expected to have a basic understanding of how to put fermions on a…
We propose a systematic procedure for the approximation of density functionals in density functional theory that consists of two parts. First, for the efficient approximation of a general density functional, we introduce an efficient ansatz…
We compare the fixed-phase approximation with the better known, but closely related fixed-node approximation on several testing examples. We found that both approximations behave very similarly with the fixed-phase results being very close…
We analyze a system of fermions in a one-dimensional harmonic trap with attractive delta-interactions between different fermions species, as an approximate description of experiments involving atomic dimers. We solve the problem of two…
We discuss techniques of the density matrix renormalization group and their application to interacting fermion systems in more than one dimension. We show numerical results for equal--time spin--spin and singlet pair field correlation…
A general field-theoretical description of many-fermion systems, with or without quenched disorder, is developed. Starting from the Grassmannian action for interacting fermions, we first bosonize the theory by introducing composite matrix…
A many-body system of fermion atoms with a model interaction characterized by the scattering length $a$ is considered. We treat both $a$ and the density as parameters assuming that the system can be created artificially in a trap. If $a$ is…
We use scaling and renormalization-group techniques to analyze the leading nonanalyticities in a Fermi liquid. We show that a physically motivated scaling hypothesis reproduce the results known from perturbation theory for the density of…
A variational formulation for the calculation of interacting fermion systems based on the density-matrix functional theory is presented. Our formalism provides for a natural integration of explicit many-particle effects into standard…
We study a one-dimensional two-component Fermi gas in a harmonic trapping potential using finite temperature lattice quantum Monte Carlo methods. We are able to compute observables in the canonical ensemble via an efficient projective…
Strongly correlated Fermi systems are among the most intriguing, best experimentally studied and fundamental systems in physics. These are, however, in defiance of theoretical understanding. The ideas based on the concepts like Kondo…
We present a variational density matrix approach to the thermal properties of interacting fermions in the continuum. The variational density matrix is parametrized by a permutation equivariant many-body unitary transformation together with…