Possible Critical Behavior Driven By Confining Potential In Optical Lattices With Ultra-Cold Fermions.pdf

The article by Campo et al. (2009) investigates the behavior of the ground-state energy per site in optical lattices with ultra-cold fermions, building upon a recent proposal for determining the phase diagram of the fermionic Hubbard model. The authors focus on the impact of the confining potential's shape, represented by parameters L and a, on the system's intensive quantities.

Key points:

- Hubbard Model: A simplified model describing correlated fermions, crucial in condensed matter physics, despite its unsolved phase diagram in dimensions greater than 2.

- Cold-Atom Experiments: Offer advantages like tunable interaction strength and hopping amplitude, large particle numbers, and easily measurable energies.

- Confinement: In solid-state systems, confinement is hard-wall type; in cold-atom experiments, it's harmonic due to external electromagnetic fields.

- Two-Parameter Scaling Method: Proposes using L and a (confinement shape) to extract the homogeneous ('hard-wall') phase diagram from inhomogeneous systems. Empirically observed that convergence rates depend on potential shape.

- Critical Behavior: During the second extrapolation (towards the homogeneous limit), they observe signatures of critical behavior related to the confining potential's shape.

- Intensive Quantities: Focus on energy per site (Ea=2L) and filling fraction (f = Na/2L).

- Experimental Relevance: Discusses generating trap potentials with varying exponents through laser beam superpositions, addressing experimental challenges.