One-dimensional repulsive Fermi gas in a tunable periodic potential

Abstract

By using unbiased continuos-space quantum Monte Carlo simulations, we investigate the ground state properties of a one-dimensional repulsive Fermi gas subjected to a commensurate periodic optical lattice (OL) of arbitrary intensity. The equation of state and the magnetic structure factor are determined as a function of the interaction strength and of the OL intensity. In the weak OL limit, Yang's theory for the energy of a homogeneous Fermi gas is recovered. In the opposite limit (deep OL), we analyze the convergence to the Lieb-Wu theory for the Hubbard model, comparing two approaches to map the continuous-space to the discrete-lattice model: the first is based on (noninteracting) Wannier functions, the second effectively takes into account strong-interaction effects within a parabolic approximation of the OL wells. We find that strong antiferromagnetic correlations emerge in deep OLs, and also in very shallow OLs if the interaction strength approaches the TonksGirardeau limit. In deep OLs we find quantitative agreement with density matrix renormalization group calculations for the Hubbard model. The spatial decay of the antiferromagnetic correlations is consistent with quasi long-range order even in shallow OLs, in agreement with previous theories for the half-filled Hubbard model.Making unbiased predictions for the properties of strongly correlated Fermi systems is one of the major challenges in quantum physics research. One dimensional systems play a central role in this context since, on the one hand, correlations effects are more pronounced in low dimensions and, on the other hand, exact results have been derived in a few relevant cases [1]. Two such cases are the homogeneous Fermi gas, whose exact ground-state energy was first determined by Yang [2] via the Bethe Anstatz technique, and the single-band Hubbard model, whose solution was provided by Lieb and Wu [3]. These two paradigmatic models describe two opposite limits of realistic physical systems, which in general are neither perfectly homogeneous nor devoid of interband couplings. In the absence of exact analytical theories for the more realistic intermediate regime, developing unbiased computational techniques is of outmost importance. The experiments performed with ultracold atoms trapped in optical lattices (OLs) have emerged as the ideal playground to investigate quantum many-body phenomena in periodic potentials [4]. The intensity of the external periodic field can be easily varied by tuning a laser power, and also the interaction strength can by tuned exploiting Feshbach resonances [5]. This has recently allowed the remarkable observation of antiferromagnetic correlations in a controlled experimental setup, both in two and in one dimension [6][7][8][9][10][11][12]. The bulk of early research activity on OL systems focussed on deep OLs and weak interactions, where single-band tight-binding models are adequate [13]. Away from this regime multi-band processes come into play, and the effect of the independent tuning of the OL intensity and the in...

Itinerant ferromagnetism in the repulsive Hubbard chain with anisotropic odd-wave attraction

“…In particular, we have shown that the double occupancy, which is experimentally accessible with cold-atom systems, is a key quantity to investigate phase separation and the formation of different ferromagnetic phases. Our findings can serve as a guide for future cold-atom experiments focussing on itinerant ferromagnetism in one-dimensional optical lattices with p-wave resonant interactions, and they complement previous studies on anti-ferromagnetic correlations in optical lattices [10,[48][49][50].…”

Out-of-equilibrium dynamics of repulsive Fermi gases in quasiperiodic potentials: A density functional theory study

“…It is worth emphasizing that, as opposed to the Aubry-André model -for which all eigenstates localize at the same quasi-disorder strength-in the continuousspace model of Eq. ( 1) the critical quasi-disorder strength depends on the energy of the state [26][27][28]39]. In particular, the low energy eigenstates localize at weaker quasidisorder strength compared to high energy states.…”

“…We focus on a halffilled lattice, with N ↑ = N ↓ = 72 particles (unless otherwise specified), so that on average there is one fermion per well of the short-period lattice. It has been recently shown that, in a single half-filled OL, interparticle interactions play an important role, causing the formation of quasi long-range antiferromagnetic order [39]. It is also worth emphasizing that a system comprising N = 144 fermions cannot be addressed via exact diagonalization calculations (see, e.g., the Krylov subspace technique of Ref.…”

One-dimensional SU(N) clusters of fermions in optical lattices

“…We consider a cluster to be in an insulating state when there is a set of at least three consecutive sites for which κ i =0 [25]. According to equation (11), this means an array of sites for which the population is the same. That set of sites would constitute an insulating domain.…”

“…Those systems were traditionally described by the discrete Hubbard model, in which the atoms are confined to the absolute minima of the laser-induced potential wells. This approximation, even though computationally very efficient, is known to break down for shallow optical lattices, both for bosons [10] and fermions [11]. Another possibility is to use the Heisenberg model, also a discrete approximation.…”