Néel Transition of Lattice Fermions in a Harmonic Trap: A Real-Space Dynamic Mean-Field Study

We study the magnetic ordering transition for a system of harmonically trapped ultracold fermions with repulsive interactions in a cubic optical lattice, within a real-space extension of dynamical mean-field theory. Using a quantum Monte Carlo impurity solver, we establish that antiferromagnetic correlations are signaled, at strong coupling, by an enhanced double occupancy. This signature is directly accessible experimentally and should be observable well above the critical temperature for long-range order. Dimensional aspects appear less relevant than naively expected.

Figure 1

First row: AF order in central plane of atomic cloud (in cubic optical lattice) for intermediate coupling $U=W=12t$. At low $T\lesssim 0.2t$ (left column), a large AF core is strongly polarized (nearly 90%); with increasing $T$, both extent and magnitude of the AF order decay. Second row: the double occupancy (top half: central density, bottom half: column density) is strongly enhanced in AF regions; in contrast, the density (3rd row, top: central, bottom: column) shows little $T$ dependence. 4th row: entropy densities (top: central, bottom: column).

Figure 2

Illustration of mechanism for enhanced double occupancy (at strong coupling) in the AF state (a) compared to a paramagnetic state (b); see text. (c) DMFT-QMC estimates of double occupancy at half filling versus $T$ for various interactions $U$; arrows indicate corresponding Néel temperatures. Thin lines: results for metastable paramagnetic phase. (d) same data scaled to values of critical point.

Figure 3

Radial dependence of staggered magnetization (top row) and double occupancy (bottom row) for $V=0.05t$ at temperature $T=0.25t$ (left column) and $T=0.42t$ (right column). The central row shows the relative enhancement of $D$ in the AF phase. Thick lines correspond to RDMFT data; thin lines represent LDA results in (a)–(d) and paramagnetic calculations in (e)–(f).

Figure 4

Fraction of atoms on doubly occupied lattice sites as a function of squared temperature; circles represent RDMFT results for the full cloud; polygons correspond to measurements along a Gaussian beam of radius $R$, as illustrated in the inset. Thick lines are quadratic fits for $(T/t{)}^2\ge (T_N/t{)}^2\approx 0.21$ (and guides to the eye below); their extrapolations $T\to 0$ are shown as thin lines.