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Register a new userTemperature dependence of spectral functions for the one-dimensional Hubbard model: comparison with experiments
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We study the temperature dependence of the single particle spectral function as well as of the dynamical spin and charge structure factors for the one-dimensional Hubbard model using the finite temperature auxiliary field quantum Monte Carlo algorithm. The parameters of our simulations are chosen so to at best describe the low temperature photoemission spectra of the organic conductor TTF-TCNQ. Defining a magnetic energy scale, T_J, which marks the onset of short ranged 2k_f magnetic fluctuations, we conclude that for temperatures T < T_J the ground state features of the single particle spectral function are apparent in the finite temperature data. Above T_J spectral weight transfer over a scale set by the hopping t is observed. In contrast, photoemission data points to a lower energy scale below which spectral weight transfer occurs. Discrepancies between Hubbard model calculations and experiments are discussed.
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We study the charge conductivity of the one-dimensional repulsive Hubbard model at finite temperature using the method of dynamical quantum typicality, focusing at half filling. This numerical approach allows us to obtain current autocorrelation functions from systems with as many as 18 sites, way beyond the range of standard exact diagonalization. Our data clearly suggest that the charge Drude weight vanishes with a power law as a function of system size. The low-frequency dependence of the conductivity is consistent with a finite dc value and thus with diffusion, despite large finite-size effects. Furthermore, we consider the mass-imbalanced Hubbard model for which the charge Drude weight decays exponentially with system size, as expected for a non-integrable model. We analyze the conductivity and diffusion constant as a function of the mass imbalance and we observe that the conductivity of the lighter component decreases exponentially fast with the mass-imbalance ratio. While in the extreme limit of immobile heavy particles, the Falicov-Kimball model, there is an effective Anderson-localization mechanism leading to a vanishing conductivity of the lighter species, we resolve finite conductivities for an inverse mass ratio of $eta gtrsim 0.25$.
We study finite-temperature transport properties of the one-dimensional Hubbard model using the density matrix renormalization group. Our aim is two-fold: First, we compute both the charge and the spin current correlation function of the integrable model at half filling. The former decays rapidly, implying that the corresponding Drude weight is either zero or very small. Second, we calculate the optical charge conductivity sigma(omega) in presence of small integrability-breaking next-nearest neighbor interactions (the extended Hubbard model). The DC conductivity is finite and diverges as the temperature is decreased below the gap. Our results thus suggest that the half-filled, gapped Hubbard model is a normal charge conductor at finite temperatures. As a testbed for our numerics, we compute sigma(omega) for the integrable XXZ spin chain in its gapped phase.
The energy gap of correlated Hubbard clusters is well studied for one-dimensional systems using analytical methods and density-matrix-renormalization-group (DMRG) simulations. Beyond 1D, however, exact results are available only for small systems by quantum Monte Carlo. For this reason and, due to the problems of DMRG in simulating 2D and 3D systems, alternative methods such as Green functions combined with many-body approximations (GFMBA), that do not have this restriction, are highly important. However, it has remained open whether the approximate character of GFMBA simulations prevents the computation of the Hubbard gap. Here we present new GFMBA results that demonstrate that GFMBA simulations are capable of producing reliable data for the gap which agrees well with the DMRG benchmarks in 1D. An interesting observation is that the accuracy of the gap can be significantly increased when the simulations give up certain symmetry restriction of the exact system, such as spin symmetry and spatial homogeneity. This is seen as manifestation and generalization of the symmetry dilemma introduced by Lowdin for Hartree--Fock wave function calculations.
We study the one-dimensional Anderson-Hubbard model using the density-matrix renormalization group method. The influence of disorder on the Tomonaga-Luttinger liquid behavior is quantitatively discussed. Based on the finite-size scaling analysis of density-density correlation functions, we find the following results: i) the charge exponent is significantly reduced by disorder at low filling and near half filling, ii) the localization length decays as $xi sim Delta^{-2}$, where $Delta$ is the disorder strength, independently of the on-site Coulomb interaction as well as band filling, and iii) the localization length is strongly suppressed by the on-site Coulomb interaction near half filling in association with the formation of the Mott plateaus.
We investigate the $T=0$ phase diagram of a variant of the one-dimensional extended Hubbard model where particles interact via a finite-range soft-shoulder potential. Using Density Matrix Renormalization Group (DMRG) simulations, we evidence the appearance of Cluster Luttinger Liquid (CLL) phases, similarly to what first predicted in a hard-core bosonic chain [M. Mattioli, M. Dalmonte, W. Lechner, and G. Pupillo, Phys. Rev. Lett. 111, 165302]. As the interaction strength parameters change, we find different types of clusters, that encode the order of the ground state in a semi-classical approximation and give rise to different types of CLLs. Interestingly, we find that the conventional Tomonaga Luttinger Liquid (TLL) is separated by a critical line with a central charge $c=5/2$, along which the two (spin and charge) bosonic degrees of freedom (corresponding to $c=1$ each) combine in a supersymmetric way with an emergent fermionic excitation ($c=1/2$). We also demonstrate that there are no significant spin correlations.
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