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]

We present a numerical study of the many-body localization (MBL) phenomenon in the high-temperature limit within an anisotropic Heisenberg model with random local fields. Taking the dynamical spin conductivity σ(ω) as the test quantity, we investigate the full frequency dependence of sample-to-sample fluctuations and their scaling properties as a function of the system size L ≤ 28 and the frequency resolution. We identify differences between the general interacting case ∆ > 0 and the anisotropy ∆ = 0, the latter corresponding to the standard Anderson localization. Except for the extreme MBL case when the relative sample-to-sample fluctuations became large, numerical results allow for the extraction of the low-ω dependence of the conductivity. Results for the d.c. value σ0 indicate a crossover into the MBL regime, i.e. an exponential-like variation with the disorder strength W . For the same regime, our numerical analysis indicates that the low-frequency exponent α exhibits a small departure from α ∼ 1 only.

Two-dimensional density-matrix renormalization group method is employed to examine the ground state phase diagram of the Hubbard model on the triangular lattice at half-filling. The calculation reveals two discontinuities in the double occupancy with increasing the repulsive Hubbard interaction U at Uc1 ∼ 7.8t and Uc2 ∼ 9.9t (t being the hopping integral), indicating that there are three phases separated by first order transitions. The absence of any singularity in physical quantities for 0 ≤ U < Uc1 implies a metallic phase in this regime. For U > Uc2, the local spin density induced by an applied pinning magnetic field exhibits a three sublattice feature, which is compatible with the 120 • Néel ordered state realized in the limit of U → ∞. For Uc1 < U < Uc2, a response to the applied pinning magnetic field is comparable to that in the metallic phase with a relatively large spin correlation length, but showing neither valence bond nor chiral magnetic order, which therefore resembles gapless spin liquid. However, the spin structure factor for the intermediate phase exhibits the maximum at the K and K points in the momentum space, which is not compatible to spin liquid with a large spinon Fermi surface. The calculation also finds that the pairing correlation function monotonically decreases with increasing U and thus the superconductivity is unlikely in the intermediate phase.arXiv:1606.06814v2 [cond-mat.str-el]

Thermodynamic properties of the Hubbard model on the anisotropic triangular lattice at half filling are calculated by the finite-temperature Lanczos method. The charge susceptibility exhibits clear signatures of a metalMott insulator transition. The metallic phase is characterized by a small charge susceptibility, large entropy, large renormalized quasiparticle mass, and large spin susceptibility. The fluctuating local magnetic moment in the metallic phase is large and comparable to that in the insulating phase. These bad metallic characteristics occur above a relatively low coherence temperature, as seen in organic charge transfer salts. PACS numbers: 71.27.+a, 71.30.+h, 74.70.Kn, Remarkable observations of a possible spin liquid phase [1] and a new universality class of the metal-insulator transition [2] in organic charge transfer salts, which in addition show unconventional superconductivity [3], have increased interest in these materials. It has been argued that a proper microscopic description of these material can be given with a Hubbard model on the anisotropic triangular lattice at half filling [4]. Parameters of the model for the description of organic charge transfer salts fall into the regime of strong correlations and significant frustration of antiferromagnetic spin interactions. This is the most challenging parameter regime, where analytical approaches become unreliable, and one needs to resort to numerical techniques.In this Letter we study a range of thermodynamic properties (charge susceptibility, specific heat, entropy and spin susceptibility) of the Hubbard model on the anisotropic triangular lattice at half-filling. The model exhibits a Mott metalinsulator transition (MIT), which can be driven either by interaction strength or by frustration. We argue that the metallic phase has a strongly reduced coherence temperature T coh , below which a Fermi liquid metal with coherent quasiparticle excitations may exist. Above T coh the model is in a bad metallic regime with large local magnetic moments. We show how frustration increases the low temperature specific heat, entropy and spin susceptibility in the insulating phase. Although the charge susceptibility shows definitive signatures of the metal-insulator transition, the specific heat and spin susceptibility do not. Indeed, above T coh there appears to be little difference between the bad metal and the Mott insulator. This is similar to the dynamical mean-field theory (DMFT) picture of the transition [5, 6].Model. The Hubbard model on the anisotropic triangular lattice has the HamiltonianThe hopping parameters t ij = t for nearest neighbors in two directions of the triangular lattice, while t ij = t ′ for nearest neighbors in the third direction. c i,σ (c † i,σ ) is a fermionic annihilation (creation) operator for an electron on site i with spin σ (either ↑ or ↓). n i,σ = c † i,σ c i,σ , U is the on-site Coulomb repulsion, and µ is the chemical potential. Most of our results are presented in units of t, and we use = k B = 1. We only consider the ...

Recent experiments on cold atoms in optical lattices allow for a quantitative comparison of the measurements to the conductivity calculations in the square lattice Hubbard model. However, the available calculations do not give consistent results and the question of the exact solution for the conductivity in the Hubbard model remained open. In this letter we employ several complementary state-of-the-art numerical methods to disentangle various contributions to conductivity, and identify the best available result to be compared to experiment. We find that at relevant (high) temperatures, the self-energy is practically local, yet the vertex corrections remain rather important, contrary to expectations. The finite-size effects are small even at the lattice size 4 × 4 and the corresponding Lanczos diagonalization result is therefore close to the exact result in the thermodynamic limit. arXiv:1811.08343v4 [cond-mat.str-el]

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We consider the implications of a phenomenological model self-energy for the charge transport properties of the metallic phase of the overdoped cuprate superconductors. The self-energy is the sum of two terms with characteristic dependencies on temperature, frequency, location on the Fermi surface, and doping. The first term is isotropic over the Fermi surface, independent of doping, and has the frequency and temperature dependence characteristic of a Fermi liquid. The second term is anisotropic over the Fermi surface (vanishing at the same points as the superconducting energy gap), strongly varies with doping (scaling roughly with Tc, the superconducting transition temperature), and has the frequency and temperature dependence characteristic of a marginal Fermi liquid. Previously it has been shown this self-energy can describe a range of experimental data including angle-dependent magnetoresistance (ADMR) and quasi-particle renormalisations determined from specific heat, quantum oscillations, and angle-resolved photo-emission spectroscopy (ARPES). Without introducing new parameters and neglecting vertex corrections we show that this model self-energy can give a quantitative description of the temperature and doping dependence of a range of reported transport properties of Tl2201 samples. These include the intra-layer resistivity, the frequency dependent optical conductivity, the intra-layer magnetoresistance, and the Hall coefficient. The temperature dependence of the latter two are particularly sensitive to the anisotropy of the scattering rate and to the shape of the Fermi surface. In contrast, the temperature dependence of the Hall angle is dominated by the Fermi liquid contribution to the self-energy that determines the scattering rate in the nodal regions of the Fermi surface.

Finite-temperature local dynamical spin correlations S(nn)(ω) are studied numerically within the random spin-1/2 antiferromagnetic Heisenberg chain. The aim is to explain measured NMR spin-lattice relaxation times in BaCu(2)(Si(0.5)Ge(0.5))(2)O(7), which is the realization of a random spin chain. In agreement with experiments we find that the distribution of relaxation times within the model shows a very large span similar to the stretched-exponential form. The distribution is strongly reduced with increasing T, but stays finite also in the high-T limit. Anomalous dynamical correlations can be associated with the random singlet concept but not directly with static quantities. Our results also reveal the crucial role of the spin anisotropy (interaction), since the behavior is in contrast with the ones for the XX model, where we do not find any significant T dependence of the distribution.