Inhomogeneous gases
Ultracold gases are usually confined using optical or magnetic trapping. In any case the confining potential (usually described as harmonic) plays very often a not-negligible role in the physics of these systems and have to be taken in account in the theoretical description of cold gases because its presence can induce several effects like spatial separation of different phases for example. One possibility is to use the so called local density approximation (LDA) in which one defines a local chemical potential
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and it is possible to derive the property of the non-homogeneus system knowing the properties of the homogeneus system for a given chemical potential.
However this approach clearly cannot address properly the regions of the trap where there are phase boundaries between different phases. Real-Space DMFT (R-DMFT, see here ) is a way to overcome this limitation and join together the advantage of DMFT as a non-perturbative approach to the possibility of studying non-homogeneus systems (not necessarily in a harmonic potential).
Within r-DMFT the self-energy is still local, i.e.
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but in general site dependent, while Σi(ω)=Σ(ω) ∀i for uniform systems. This allows to describe proximity effects in the phase boundaries which are beyond the reach of LDA-type approaches.
DMFT has been used to study formation of antiferromagnetic patterns in presence of harmonic confinement in systems described by a inhomogeneus Hubbard model, whose Hamiltonian reads:
which is relevant for the description of recent and future experiments aiming to observe the Mott state using cold atoms in optical lattice.
Indeed if lower temperatures than the actual experiments are reached, it is natural to expect the formation of antiferromagnetism in the system. Here we show results for zero temperature
for a two dimensional system in a trap within r-DMFT.
The results show the existence of antiferromagnetic regions in zones close to the phase boundaries with the paramagnetic phase where the density deviates significantly from half-filling.
