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We calculate the superfluid weight and the polarization amplitude for the one-dimensional bosonic Hubbard model focusing on the strong-coupling regime. Other than analytic calculations we apply two methods: variational Monte Carlo based on the Baeriswyl wave function and exact diagonalization. The former gives zero superfluid response at integer filling, while the latter gives a superfluid response at finite hopping. From the polarization amplitude we derive the variance and the associated size scaling exponent. Again, the variational study does not produce a finite superfluid weight at integer filling (size scaling exponent is near one), but the Fourier transform of the polarization amplitude behaves in a similar way to the result of exact diagonalization, with a peak at small hopping, and suddenly decreasing at the insulator-superfluid transition. On the other hand, exact diagonalization studies result in a finite spread of the total position which increases with the size of the system. In the superfluid phase the size scaling exponent is two as expected. Importantly, our work addresses the ambiguities that arise in the calculation of the superfluid weight in variational calculations, and we comment on the prediction of Anderson about the superfluid response of the model at integer filling., Comment: rewritten, somewhat shortened in response to the critique of a referee

A variational Monte Carlo method for bosonic lattice models is introduced. The method is based on the Baeriswyl projected wavefunction. The Baeriswyl wavefunction consists of a kinetic energy based projection applied to the wavefunction at infinite interaction, and is related to the shadow wavefunction already used in the study of continuous models of bosons. The wavefunction at infinite interaction, and the projector, are represented in coordinate space, leading to an expression for expectation values which can be evaluated via Monte Carlo sampling. We calculate the phase diagram and other properties of the bosonic Hubbard model. The calculated phase diagram is in excellent agreement with known quantum Monte Carlo results. We also analyze correlation functions., minor changes compared to previous version

In this paper we show that the general finite-energy spectral-function expressions provided by the pseudofermion dynamical theory for the one-dimensional Hubbard model lead to the expected low-energy Tomonaga–Luttinger liquid correlation function expressions. Moreover, we use the former general expressions to derive correlation-function asymptotic expansions in space and time which go beyond those obtained by conformal-field theory and bosonization: we derive explicit expressions for the pre-factors of all terms of such expansions and find that they have an universal form, as the corresponding critical exponents. Our results refer to all finite values of the on-site repulsion U and to a chain of length L very large and with periodic boundary conditions for the above model, but are of general nature for many integrable interacting models. The studies of this paper clarify the relation of the low-energy Tomonaga–Luttinger liquid behavior to the scattering mechanisms which control the spectral properties at all energy scales and provide a broader understanding of the unusual properties of quasi-one-dimensional nanostructures, organic conductors, and optical lattices of ultracold fermionic atoms. Furthermore, our results reveal the microscopic mechanisms which are behind the similarities and differences of the low-energy and finite-energy spectral properties of the model metallic phase.

The momentum and energy dependence of the weight distribution in the vicinity of the one-electron spectral-function singular branch lines of the 1D Hubbard model is studied for all values of the electronic density and on-site repulsion $U$. To achieve this goal we use the recently introduced pseudofermion dynamical theory. Our predictions agree quantitatively for the whole momentum and energy bandwidth with the peak dispersions observed by angle-resolved photoelectron spectroscopy in the quasi-1D organic conductor TTF-TCNQ., Comment: Replaced with shortened version; 4 figures

In this paper we derive general expressions for few-electron spectral functions of the one-dimensional Hubbard model for values of the excitation energy in the vicinity of the Mth upper-Hubbard band lower limit. Here M = 1,2,... is the rotated-electron double occupation, which vanishes for the ground state and is a good quantum number for all values of the on-site Coulomb repulsion U. Our studies rely on a combination of symmetries of the model with a recent finite-energy holon and spinon description of the quantum problem. We apply our general scheme to the one-electron addition spectral function, dynamical structure factor and spin singlet Cooper-pair addition spectral function. Our results provide physically interesting information about the finite-energy spectral properties of the many-electron one-dimensional quantum liquid.

The Hubbard model is investigated for a halffilled honeycomb lattice, using a variational method. Two trial wave functions are introduced, the Gutzwiller wave function, well suited for describing the “metallic” phase at small U and a complementary wave function for the insulating regime at large values of U. The comparison of the two variational ground states at the mean-field level yields a Mott transition at U c /t ≈ 5:3. In addition, a variational Monte Carlo calculation is performed in order to locate the instability of the “metallic” wave function with respect to antiferromagnetism. The critical value U m/t ≈ 3:7 obtained in this way is considered to be a lower bound for the true critical point for antiferromagnetism, whereas there are good arguments that the mean-field value U c/t ≈ 5:3 represents an upper bound for the Mott transition. Therefore the “metal”- insulator transition for the honeycomb lattice may indeed be simultaneously driven by the antiferromagnetic instability and the Mott phenomenon.

We study the electronic structure of the quasi-one-dimensional organic conductor TTF-TCNQ by means of density-functional band theory, Hubbard model calculations, and angle-resolved photoelectron spectroscopy (ARPES). The experimental spectra reveal significant quantitative and qualitative discrepancies to band theory. We demonstrate that the dispersive behavior as well as the temperature-dependence of the spectra can be consistently explained by the finite-energy physics of the one-dimensional Hubbard model at metallic doping. The model description can even be made quantitative, if one accounts for an enhanced hopping integral at the surface, most likely caused by a relaxation of the topmost molecular layer. Within this interpretation the ARPES data provide spectroscopic evidence for the existence of spin-charge separation on an energy scale of the conduction band width. The failure of the one-dimensional Hubbard model for the {\it low-energy} spectral behavior is attributed to interchain coupling and the additional effect of electron-phonon interaction., 18 pages, 9 figures