We study the spin diffusion and spin conductivity in the square lattice Hubbard model by using the finite-temperature Lanczos method. We show that the spin diffusion behaves differently from the charge diffusion and has a nonmonotonic $T$ dependence. This is due to a progressive liberation of charges that contribute to spin transport and enhance it beyond that active at low temperature due to the Heisenberg exchange. We further show that going away from half-filling and zero magnetization increases the spin diffusion, but that the increase is insufficient to reconcile the difference between the model calculations and the recent measurements on cold-atoms.
We study the frequency and temperature dependence of the optical conductivity in the weakly coupled two-dimensional Hubbard model using a renormalized perturbative expansion. The perturbative expansion is based on the skeleton series for the current-current correlation function with a dressed Green`s function and the results are obtained directly on the real frequency axis using Algorithmic Matsubara Integration (AMI). The resulting conductivity shows a temperature-independent power law behaviour in the intermediate frequency regime. Moreover, the associated transport scattering time and renor…
We consider the optical conductivity in the one dimensional Hubbard model in the metallic phase close to half filling. In this regime most of the spectral weight is located at frequencies above an energy scale $E_{\rm opt}$ that tends towards the optical gap in the Mott insulating phase for vanishing doping. Using the Bethe Ansatz we relate $E_{\rm opt}$ to thresholds of particular kinds of excitations in the Hubbard model. We then employ a mobile impurity models to analyze the optical conductivity for frequencies slightly above these thresholds. This entails generalizing mobile impurity model…
Calculation of conductivity in the Hubbard model is a challenging task. Recent years have seen much progress in this respect and numerically exact solutions are now possible in certain regimes. In this paper we discuss the calculation of conductivity for the square lattice Hubbard model in the presence of a perpendicular magnetic field, focusing on orbital effects. We present the relevant formalism in all detail and in full generality, and then discuss the simplifications that arise at the level of the dynamical mean field theory (DMFT). We prove that the Kubo bubble preserves gauge and transl…
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 sel…
Nonlocal Correlation Effects in dc and Optical Conductivity of the Hubbard Model
Universität Hamburg（汉堡大学）；Orebro University（厄勒布鲁大学）；The Hamburg Centre for Ultrafast Imaging（汉堡超快成像中心）；European X-Ray Free-Electron Laser Facility（欧洲X射线自由电子激光设施）；CNRS, École polytechnique, Institut Polytechnique de Paris（法国国家科学研究中心，巴黎综合理工学院，巴黎理工学院）；Collège de France（法兰西公学院）
We compute the frequency dependent conductivity of the two dimensional square lattice Hubbard model at zero temperature as a function of density to second order in the interaction strength, and compare the results to the predictions of single-site dynamical mean field theory computed at the same order. We find that despite the neglect of vertex corrections, the single site dynamical mean field approximation produces semiquantitatively accurate results for most carrier concentrations, but fails qualitatively for the nearly empty or nearly filled band cases where the theory exhibits an emergent …
The optical conductivity contains information about energy absorption and the underlying physical processes. In finite-dimensional systems, vertex corrections to the bare bubble need to be considered, which is a computationally challenging task. Recent numerical studies showed that in the weak coupling limit, near an ordering instability with wave vector $π$, $π$-tons (or Maki-Thompson diagrams) yield the most relevant vertex corrections. This provides a route for including vertex corrections into, for example, dynamical mean field theory estimates of the optical conductivity. By implementing …
We consider the optical conductivity $σ_1(ω)$ in the metallic phase of the one-dimensional Hubbard model. Our results focus on the vicinity of half filling and the frequency regime around the optical gap in the Mott insulating phase. By means of a density-matrix renormalization group implementation of the correction-vector approach, $σ_1(ω)$ is computed for a range of interaction strengths and dopings. We identify an energy scale $E_{\rm opt}$ above which the optical conductivity shows a rapid increase. We then use a mobile impurity model in combination with exact results to determine the beha…
We study how the synergetic effect of spin-orbit coupling (SOC) and Zeeman splitting (ZS) affects the optical conductivity in the one-dimensional Hubbard model using the Kubo formula. We focus on two phenomena: (1) the electric dipole spin resonance (EDSR) in the metallic regime and (2) the optical conductivity in the Mott-insulating phase above the optical gap. In both cases, we calculate qualitatively the effects of SOC and ZS and how they depend on the relative angle between the SOC vector and the magnetic field direction. First, we investigate the spin resonance without electron correlatio…
Exact diagonalization study of optical conductivity in two-dimensional Hubbard model
本文应用精确对角化技术研究了二维哈伯德模型中具有周期性边界条件的正方形团簇直到\sqrt{20} X \sqrt{20}格点的光学电导率σ（ω）。20格点团簇的半填充谱分布及其掺杂依赖性与\sqrt{18} X \sqrt{18}团簇相似，但与4 X 4团簇不同.的20个站点的集群的结果使我们能够进行系统的研究的掺杂的光谱重量转移从该区域的莫特间隙激发到较低的能量区域的依赖。我们讨论了在大的在位库仑相互作用下，Drude重量和有效载流子数对电子密度的依赖关系。
We numerically study optical conductivity $σ(ω)$ near the "antiferromagnetic" phase transition in the square-lattice Hubbard model at half filling. We use a cluster dynamical mean field theory and calculate conductivity including vertex corrections, and to this end, we have reformulated the vertex corrections in the antiferromagnetic phase. We find that the vertex corrections change various important details in temperature- and $ω$-dependencies of conductivity in the square lattice, and this contrasts sharply the case of the Mott transition in the frustrated triangular lattice. Generally, the …
We study the electronic thermal conductivity $κ_\textrm{el}$ and the thermal diffusion constant $D_\textrm{Q,el}$ in the square lattice Hubbard model using the finite-temperature Lanczos method. We exploit the Nernst-Einstein relation for thermal transport and interpret the strong non-monotonous temperature dependence of $κ_\textrm{el}$ in terms of that of $D_\textrm{Q,el}$ and the electronic specific heat $c_\textrm{el}$. We present also the results for the Heisenberg model on a square lattice and ladder geometries. We study the effects of doping and consider the doped case also with the dyna…
We study experimentally the Raman response of the undoped high-Tc parent compound $YBa_2Cu_3O_6$, and give a unified theory of the two-magnon Raman peak and optical conductivity based on the Hubbard-Holstein model with electron-phonon coupling (EPC). The Hubbard model without EPC can qualitatively account for the experimentally observed resonance of the Raman response, but only the Hubbard-Holstein model (i) reproduces asymmetry of the Raman spectrum, (ii) validates experimental visibility of the two-magnon peak, and (iii) predicts the correct shape and energy of the lower edge of the charge t…
The optical conductivity of half-filled Hubbard ladders
我们研究了半填充N-腿哈伯德阶梯的光学电导率远到“去精细”极限（即，弱Hubbard相互作用和相对强的链间跳跃）。N-leg Hubbard阶梯等效于速度服从$v_1=v_N<v_2=v_{N-1}<...$的N带模型。当N不是太大的$(N=3,4...)$时，带对$(i,N+1-i)$连续地流向D-Mott态，导致电荷和自旋间隙的级联[U. Ledermann，K. Le Hur和T. M. Rice，Phys. Rev. B { \bf{62} }，16383（2000）]，以及二维（2D）费米表面（FS）的逐渐闭合。在有限温度下的光学电导率可以表现出一个突出的德鲁德峰和一个高频预制对连续谱之间的共存，分裂尖锐的激子峰产生由于近似SO（8）对称性。对于非常大（但有限）的N，所有相邻的带在2D FS上相互作用，导致低温2D莫特交叉伴随着自旋密度波（SDW）不稳定性（类似于2D情况）。在此极限下，光学电导率呈现出独特的电荷间隙-间隙上方的激发被束缚空穴对-并且激子特征消失。这些结果可以帮助解释的光学电导率的2D系统在和接近半填充，其中的一个例子是高- $T_c$铜酸盐的赝隙相。
Optical and Hall conductivity of the two dimensional Hubbard model: effective theory description, sign-problem-free Monte Carlo simulation and applications to the cuprate superconductors
School of Physics, Renmin University of China（中国人民大学物理学院）
We study the thermal conductivity of the one-dimensional Fermi-Hubbard model at finite temperature using a density matrix renormalization group approach. The integrability of this model gives rise to ballistic thermal transport. We calculate the temperature dependence of the thermal Drude weight at half filling for various interactions and moreover, we compute its filling dependence at infinite temperature. The finite-frequency contributions originating from the fact that the energy current is not a conserved quantity are investigated as well. We report evidence that breaking the integrability…
We study the Haldane-Hubbard model by exact Renormalization Group techniques. We construct the topological phase diagram, for weak interactions. We predict that many-body interactions induce a shift of the transition line. The presence of new intermediate phases, absent in the non interacting case, is rigorously excluded at weak coupling. Despite the nontrivial renormalization of the wave function and of the Fermi velocity, the conductivity is universal: at the renormalized critical line, both the discontinuity of the transverse conductivity and the longitudinal conductivity do not depend on t…
We investigate the spin Seebeck coefficient $S_s$ in the square lattice Hubbard model at high temperatures of relevance to cold-atom measurements. We solve the model with the finite-temperature Lanczos and with the dynamical mean-field theory methods and find they give similar results in the considered regime. $S_s$ exceeds the atomic 'Heikes' estimates and the Kelvin entropic estimates drastically. We analyze the behavior in terms of a mapping onto the problem of a doped attractive model and derive an approximate expression that allows relating the enhancement of $S_s$ to distinct scattering …
Low-energy photoexcitations inside the Mott gap in doped Hubbard and t-J ladders
Tokyo University of Science（东京科学大学）；Mawlana Bhashani Science and Technology University（毛拉纳·巴沙尼科学技术大学）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所新兴物质科学中心）；RIKEN Center for Computational Science (R-CCS)（理化学研究所计算科学中心）；RIKEN Center for Quantum Computing (RQC)（理化学研究所量子计算中心）；RIKEN Cluster for Pioneering Research (CPR)（理化学研究所先锋研究集群）
