Local density fluctuation approach to Fermionic lattice models

Zhengqian Cheng, Chris A. Marianetti

Román López-Sandoval, G. M. Pastor

Atsushi Yamamoto, Makoto Yamashita, Norio Kawakami

We study the ground state properties of ultracold fermions trapped in a one-dimensional double-well optical lattice by using the density-matrix renormalization group method. The system is described by an extended Hubbard model with alternating hopping integrals and an external harmonic confining potential. We clarify the characteristic features of the metal–insulator phase transition originating from the double-well structure of the lattices. Several different types of insulating regions coexist when the number of atoms at each site is an integer or a half integer. We found that each insulating phase except for a band insulator exhibits rather large local density fluctuations, reflecting the strong dimerization of atoms within the unit cells of double-well lattices. The phase characteristics are elucidated in detail by investigating the profiles of the local density of atoms, the local density (spin) fluctuations, the double-occupancy probability and the spatially extended sp in correlations.

C. Lavalle, Marcos Rigol, Alejandro Muramatsu

Abstract The cover picture of the current issue, taken from the Feature Article [1], depicts the evolution of local density (a) and its quantum fluctuations (b) in trapped fermions on one‐dimensional optical lattices. As the number of fermions in the trap is increased, figure (a) shows the formation of a Mott‐insulating plateau (local density equal to one) whereas the quantum fluctuations – see figure (b) – are strongly suppressed, but nonzero. For a larger number of fermions new insulating plateaus appear (this time with local density equal to two), but no density fluctuations. Regions with non‐constant density are metallic and exhibit large quantum fluctuations of the density. The first author Catia Lavalle is a Postdoc at the University of Stuttgart. She works in the field of strongly correlated quantum systems by means of Quantum Monte Carlo methods (QMC). While working on her PhD thesis at the University of Stuttgart, she developed a new QMC technique that allows to study dynamical properties of the t–J model.

Zhengqian Cheng, Chris A. Marianetti

J. H. Drewes, Eugenio Cocchi, Luke A. Miller +4 more

The crossover between a metal and a Mott insulator leads to a localization of fermions from delocalized Bloch states to localized states. We experimentally study this crossover using fermionic atoms in an optical lattice by measuring thermodynamic and local (on-site) density correlations. In the metallic phase at incommensurable filling we observe the violation of the local fluctuation-dissipation theorem indicating that the thermodynamics of the system cannot be characterized by local observables alone. In contrast, in the Mott insulator we observe the convergence of local and thermodynamic fluctuations indicating the absence of long-range density-density correlations.