Seminar Bloch group Munich 2011/05/03

Double occupancy as a universal probe for antiferromagnetic correlations and entropy in cold fermions on optical lattices

Ultracold fermionic atoms on optical lattices have been proposed as quantum simulators of correlated solids, i.e. tools for shedding light on poorly understood low-temperature phases such as high-T_c superconductivity. A missing link towards this goal is the realization of antiferromagnetic (AF) Néel phases: in spite of extensive efforts no AF signatures have been seen in experiments yet. This failure is commonly attributed to cooling issues. Indeed, the coldest systems achieved so far have central entropies per particle of s=s/(N k_B)≈ log(2) while AF long-range order is expected in a cubic system only for s<log(2)/2.

In my talk I will argue, based on new theoretical results, that this discrepancy is not really relevant for the experiments currently performed or prepared in this context: both modulation spectroscopy [1] and the superlattice approach [2] address the nearest-neighbor correlation function, similarly to the double occupancy which we have recently suggested as a signature of AF correlations [3]. Specifically, I will briefly introduce the relevant theoretical concepts,including our quantum Monte Carlo (QMC) based implementation [4] of real-space dynamical mean-field theory (DMFT), and show that (i) the development of (local) AF order at low T and strong coupling is accompanied, within DMFT, by a distinct enhancement of the double occupancy D; (ii) the local density approximation is insufficient for ordered phases [3].

I will then show, by comparisons with direct determinantal QMC calculations, that this DMFT scenario applies even in two dimensions, for which the Néel temperature is zero, and is precise on the percent level, up to rounding effects, for a cubic optical lattice. As a function of entropy s, D is nearly universal with respect to dimensionality; in particular, the minimum in D(s) always occurs at s ≈ log(2) at strong coupling, as predicted by DMFT. Long-range order appears irrelevant for the current search of AF signatures in cold fermions. Thus, experimentalists need not achieve s < log(2)/2 and should consider lower dimensions, for which the AF effects are larger.

[1] Daniel Greif, Leticia Tarruell, Thomas Uehlinger, Robert Jördens, and Tilman Esslinger, Phys. Rev. Lett. 106, 145302 (2011).
[2] S. Trotzky, Yu-Ao Chen, U. Schnorrberger, P. Cheinet, and I. Bloch, Phys. Rev. Lett. 105, 265303 (2010).
[3] E. V. Gorelik, I. Titvinidze, W. Hofstetter, M. Snoek, and N. Blümer, Phys. Rev. Lett. 105, 065301 (2010).
[4] N. Blümer and E. V. Gorelik, Computer Physics Communications 118, 115 (2011).