The repulsive Hubbard Hamiltonian is one of the foundational models describing strongly correlated electrons and is believed to capture essential aspects of high-temperature superconductivity. Ultracold fermions in optical lattices allow for the simulation of the Hubbard Hamiltonian with control over kinetic energy, interactions, and doping. A great challenge is to reach the required low entropy and to observe antiferromagnetic spin correlations beyond nearest neighbors, for which quantum gas microscopes are ideal. Here, we report on the direct, single-site resolved detection of antiferromagnetic correlations extending up to three sites in spin-1/2 Hubbard chains, which requires entropies per particle well below s* = ln(2). The simultaneous detection of spin and density opens the route toward the study of the interplay between magnetic ordering and doping in various dimensions.

We study finite-size effects at first-order quantum transitions (FOQTs). We show that the low-energy properties show a finite-size scaling (FSS) behavior, the relevant scaling variable being the ratio of the energy associated with the perturbation driving the transition and the finite-size energy gap at the FOQT point. The size dependence of the scaling variable is therefore essentially determined by the size dependence of the gap at the transition, which in turn depends on the boundary conditions. Our results have broad validity and, in particular, apply to any FOQT characterized by the degeneracy and crossing of the two lowest-energy states in the infinite-volume limit. In this case, a phenomenological two-level theory provides exact expressions for the scaling functions. Numerical results for the quantum Ising chain in transverse and parallel magnetic fields support the FSS Ansätzes.

The interplay between magnetism and doping is at the origin of exotic strongly correlated electronic phases and can lead to novel forms of magnetic ordering. One example is the emergence of incommensurate spin-density waves with a wave vector that does not match the reciprocal lattice. In one dimension this effect is a hallmark of Luttinger liquid theory, which also describes the low energy physics of the Hubbard model [1]. Here we use a quantum simulator based on ultracold fermions in an optical lattice [2-8] to directly observe such incommensurate spin correlations in doped and spin-imbalanced Hubbard chains using fully spin and density resolved quantum gas microscopy. Doping is found to induce a linear change of the spin-density wave vector in excellent agreement with Luttinger theory predictions. For non-zero polarization we observe a decrease of the wave vector with magnetization as expected from the Heisenberg model in a magnetic field. We trace the microscopic origin of these incommensurate correlations to holes, doublons and excess spins which act as delocalized domain walls for the antiferromagnetic order. Finally, when inducing interchain coupling we observe fundamentally different spin correlations around doublons indicating the formation of a magnetic polaron [9]. arXiv:1803.08892v1 [cond-mat.quant-gas]

We study a mixture of two superfluids with density-density and current-current (Andreev-Bashkin) interspecies interactions. The Andreev-Bashkin coupling gives rise to a dissipationless drag (or entrainment) between the two superfluids. Within the quantum hydrodynamics approximation, we study the relations between speeds of sound, susceptibilities and static structure factors, in a generic model in which the density and spin dynamics decouple. Due to translational invariance, the density channel does not feel the drag. The spin channel, instead, does not satisfy the usual Bijl-Feynman relation, since the f-sum rule is not exhausted by the spin phonons. The very same effect on one dimensional Bose mixtures and their Luttinger liquid description is analysed within perturbation theory. Using diffusion quantum Monte Carlo simulations of a system of dipolar gases in a double layer configuration, we confirm the general results. Given the recent advances in measuring the counterflow instability, we also study the effect of the entrainment on the dynamical stability of a superfluid mixture with non-zero relative velocity.