Interaction-Induced Adiabatic Cooling and Antiferromagnetism of Cold Fermions in Optical Lattices

We propose an interaction-induced cooling mechanism for two-component cold fermions in an optical lattice. It is based on an increase of the spin entropy upon localization, an analogue of the Pomeranchuk effect in liquid helium 3. We discuss its application to the experimental realization of the antiferromagnetic phase. We illustrate our arguments with dynamical mean-field theory calculations.

Figure 1

Phase diagram of the half-filled Hubbard model on the cubic lattice: antiferromagnetic (AF) and paramagnetic (PM) phases. Transition temperature within DMFT approximation (solid curve, open circles) and QMC calculation of Ref. 13 (dot-dashed curve, squares). Dashed lines: isentropic curves ($s=0.4$, 0.7, 0.75, 0.8), computed within DMFT. Dotted line: quasiparticle coherence scale $T_F^{*}(U)$. The DMFT results were obtained with QMC calculations (for $T_N$) and the IPT approximation [11] (for the isentropics). The transition curves are interpolations, continued at high $U/t$ using the analytical expressions for the Heisenberg regime.

Figure 2

Double occupancy $d=⟨n_{i\uparrow }{n}_{i\downarrow }⟩$ as a function of temperature, for several values of $U/t$, calculated within DMFT (IPT). The initial decrease is the Pomeranchuk effect responsible for adiabatic cooling.

Figure 3

Phase diagram as a function of entropy. The displayed curve results from a DMFT-IPT calculation (in which case $s_H=\ln 2$), but its shape is expected to be general (with $s_H$ reduced by quantum fluctuations).

Figure 4

Spin-density wave and Heisenberg regimes as a function of the depth of the periodic potential $V_0$ and the scattering length $a_s$. The crossover between these regimes is indicated by the dotted line ($U/t=10$), where $T_N/t$ is maximum (other contour lines are also indicated). In the shaded region, the one-band Hubbard description is no longer valid. Above the dashed line ($U/\Delta >0.1$), other bands must be taken into account and the pseudopotential approximation fails. Above the dashed-dotted line, non-Hubbard interaction terms become sizeable ($t_d/t>0.1$, see text).