Strong interactions in many-body quantum systems complicate the interpretation of charge transport in such materials. To shed light on this problem, we study transport in a clean quantum system: ultracold 6 Li in a 2D optical lattice, a testing ground for strong interaction physics in the Fermi-Hubbard model. We determine the diffusion constant by measuring the relaxation of an imposed density modulation and modeling its decay hydrodynamically. The diffusion constant is converted to a resistivity using the Nernst-Einstein relation. That resistivity exhibits a linear temperature dependence and shows no evidence of saturation, two characteristic signatures of a bad metal. The techniques we develop here may be applied to measurements of other transport quantities, including the optical conductivity and thermopower. arXiv:1802.09456v2 [cond-mat.quant-gas]
The first indication of a pseudogap in cuprates came from a sudden decrease of NMR Knight shift at a doping-dependent temperature T * (δ). Since then, experiments have found phase transitions at a lower T * phase (δ). Using plaquette cellular dynamical mean-field for the square-lattice Hubbard model at high temperature, where the results are reliable, we show that T * (δ) shares many features of T * phase (δ). The remarkable agreement with several experiments, including quantum critical behavior of the electronic specific heat, supports the view that the pseudogap is controlled by a finite-doping extension of the Mott transition. We propose further experimental tests. PACS numbers: 71.30.+h, 74.25.Dw, 71.10.Fd Below a doping-dependent temperature T * , early studies of cuprate high temperature superconductors found a decrease in NMR Knight shift [1-5]. This freezing of uniform spin fluctuations, a thermodynamic quantity, became the first signature of what is widely referred to as the pseudogap, one of the remaining challenges for theory. With time, another definition of the pseudogap became more popular. Polarized neutron diffraction [6-8], Nernst effect measurements [9], ultrasound measurements [10], terahertz polarimetry [11] and optical anisotropy measurements [12] report that the prototypical YBa 2 Cu 3 O y undergoes a thermodynamic phase transition that breaks time-reversal, spatial inversion, twofold rotational, four-fold rotational and mirror symmetries below a doping-dependent temperature T * phase that is distinctly lower than T * at low doping. This suggests that phase transitions are a consequence of the pseudogap first observed in NMR, not the cause [13,14].In this paper, we address the nature of the pseudogap that was first found in NMR. We focus mostly on thermodynamic signatures at high temperature, where cluster generalizations of dynamical mean-field theory provide a reliable theoretical tool. The remarkable agreement that we find with several experiments supports the view that the high-temperature physics of the pseudogap is controlled by a finite-doping extension of the Mott transition that includes superexchange effects [15]. We propose further experimental tests to investigate that hypothesis.
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