Superconductivity in the repulsive Hubbard model: an asymptotically exact weak-coupling solution

We study the phase diagram of the Hubbard model in the limit where U, the onsite repulsive interaction, is much smaller than the bandwidth. We present an asymptotically exact expression for T$_c$, the superconducting transition temperature, in terms of the correlation functions of the non-interacting system which is valid for arbitrary densities so long as the interactions are sufficiently small. Our strategy for computing T$_c$ involves first integrating out all degrees of freedom having energy higher than an unphysical initial cutoff $\Omega_0$. Then, the renormalization group (RG) flows of the resulting effective action are computed and T$_c$ is obtained by determining the scale below which the RG flows in the Cooper channel diverge. We prove that T$_c$ is independent of $\Omega_0$. Using this method, we find a variety of unconventional superconducting ground states in two and three dimensional lattice systems and present explicit results for T$_c$ and pairing symmetries as a function of the electron concentration.Comment: 18 pages, 17 figure

Spin picture of the one-dimensional Hubbard model: Two-fluid structure and phase dynamics

We propose a scheme for investigating the quantum dynamics of interacting electron models by means of time-dependent variational principle and spin coherent states of space lattice operators. We apply such a scheme to the one-dimensional hubbard model, and solve the resulting equations in different regimes. In particular, we find that at low densities the dynamics is mapped into two coupled nonlinear Schroedinger equations, whereas near half-filling the model is described by two coupled Josephson junction arrays. Focusing then to the case in which only the phases of the spin variables are dynamically active, we examine a number of different solutions corresponding to the excitations of few macroscopic modes. Based on fixed point equation of the simpler among them, we show that the standard one-band ground state phase space is found.Comment: 10 pages, 1 figure, to appear on Phys. Rev.

Time dependent mean field theory of the superfluid-insulator phase transition

We develop a time-dependent mean field approach, within the time-dependent variational principle, to describe the Superfluid-Insulator quantum phase transition. We construct the zero temperature phase diagram both of the Bose-Hubbard model (BHM), and of a spin-S Heisenberg model (SHM) with the XXZ anisotropy. The phase diagram of the BHM indicates a phase transition from a Mott insulator to a compressibile superfluid phase, and shows the expected lobe-like structure. The SHM phase diagram displays a quantum phase transition between a paramagnetic and a canted phases showing as well a lobe-like structure. We show how the BHM and Quantum Phase model (QPM) can be rigorously derived from the SHM. Based on such results, the phase boundaries of the SHM are mapped to the BHM ones, while the phase diagram of the QPM is related to that of the SHM. The QPM's phase diagram obtained through the application of our approach to the SHM, describes the known onset of the macroscopic phase coherence from the Coulomb blockade regime for increasing Josephson coupling constant. The BHM and the QPM phase diagrams are in good agreement with Quantum Monte Carlo results, and with the third order strong coupling perturbative expansion.Comment: 15 pages, 8 figures. To be published in Phys. Rev.

Spin- and charge-density waves in the Hartree-Fock ground state of the two-dimensional Hubbard model

The ground states of the two-dimensional repulsive Hubbard model are studied within the unrestricted Hartree-Fock (UHF) theory. Magnetic and charge properties are determined by systematic, large-scale, exact numerical calculations, and quantified as a function of electron doping $h$. In the solution of the self-consistent UHF equations, multiple initial configurations and simulated annealing are used to facilitate convergence to the global minimum. New approaches are employed to minimize finite-size effects in order to reach the thermodynamic limit. At low to moderate interacting strengths and low doping, the UHF ground state is a linear spin-density wave (l-SDW), with antiferromagnetic order and a modulating wave. The wavelength of the modulating wave is $2/h$. Corresponding charge order exists but is substantially weaker than the spin order, hence holes are mobile. As the interaction is increased, the l-SDW states evolves into several different phases, with the holes eventually becoming localized. A simple pairing model is presented with analytic calculations for low interaction strength and small doping, to help understand the numerical results and provide a physical picture for the properties of the SDW ground state. By comparison with recent many-body calculations, it is shown that, for intermediate interactions, the UHF solution provides a good description of the magnetic correlations in the true ground state of the Hubbard model.Comment: 13 pages, 17 figure, 0 table

Bethe Ansatz solution of a new class of Hubbard-type models

We define one-dimensional particles with generalized exchange statistics. The exact solution of a Hubbard-type Hamiltonian constructed with such particles is achieved using the Coordinate Bethe Ansatz. The chosen deformation of the statistics is equivalent to the presence of a magnetic field produced by the particles themselves, which is present also in a ``free gas'' of these particles.Comment: 4 pages, revtex. Essentially modified versio

Metal-Insulator Transitions in Degenerate Hubbard Models and Ax_xC60_{60}

Mott-Hubbard metal-insulator transitions in $N$-fold degenerate Hubbard models are studied within the Gutzwiller approximation. For any rational filling with $x$ (integer) electrons per site it is found that metal-insulator transition occurs at a critical correlation energy $U_c(N,x)=U_c(N,2N-x)=\gamma(N,x)|\bar{\epsilon}(N,x)|$, where $\bar{\epsilon}$ is the band energy per particle for the uncorrelated Fermi-liquid state and $\gamma(N,x)$ is a geometric factor which increases linearly with $x$. We propose that the alkali metal doped fullerides $A_xC_{60}$ can be described by a 3-fold degenerate Hubbard model. Using the current estimate of band width and correlation energy this implies that most of ${\rm A_xC_{60}}$, at integer $x$, are Mott-Hubbard insulators and ${\rm A_3C_{60}}$ is a strongly correlated metal.Comment: 10 pages, Revte

SHBG levels in primary infertile men : A critical interpretation in clinical practice

Objective: We aimed to test the association between age, BMI and sex-hormone\u2013binding globulin (SHBG) in a homogenous cohort of white-European men presenting for primary couple\u2019s infertility. Design: Retrospective study. Methods: Data from 1547 infertile men were analysed. Health-significant comorbidities were scored with the Charlson comorbidity index (CCI). Fasting serum hormones were measured in every patient. Age was considered according to quartile groups (<33, 33-41, >41 years) and BMI as normal weight (18.5\u201324.9 kg/m2), overweight (25.0\u201329.9 kg/m2) and obesity (>30 kg/m2). Descriptive statistics and linear regression analysis tested the associations between age, BMI and SHBG. Results: Median SHBG levels increased across quartiles of age and decreased along with BMI increases (all P < 0.001). For each year increase in age, SHBG increased 0.32 nmol/L; conversely, for each unit increase in BMI, SHBG decreased by 1.1 nmol/L (all P < 0.001). SHBG levels decline with increasing BMI was greater than SHBG progressive increase with age. Overall, BMI explained 3.0 times more of the variability in SHBG than did ageing. At multivariate linear model, age and BMI were the most significant factors influencing SHBG concentration (all P < 0.001), after accounting for CCI, albumin levels and smoking status. Conclusions: We found a wide distribution of SHBG concentrations across age and BMI values in primary infertile men. The association between BMI and lowered SHBG levels seems to be greater than the association of ageing with increased SHBG

Improved stability regions for ground states of the extended Hubbard model

The ground state phase diagram of the extended Hubbard model containing nearest and next-to-nearest neighbor interactions is investigated in the thermodynamic limit using an exact method. It is found that taking into account local correlations and adding next-to-nearest neighbor interactions both have significant effects on the position of the phase boundaries. Improved stability domains for the $\eta$-pairing state and for the fully saturated ferromagnetic state at half filling have been constructed. The results show that these states are the ground states for model Hamiltonians with realistic values of the interaction parameters.Comment: 21 pages (10 figures are included) Revtex, revised version. To be published in Phys. Rev. B. E-mail: [email protected]

Asexuality: Classification and characterization

This is a post-print version of the article. The official published version can be obtaineed at the link below.The term “asexual” has been defined in many different ways and asexuality has received very little research attention. In a small qualitative study (N = 4), individuals who self-identified as asexual were interviewed to help formulate hypotheses for a larger study. The second larger study was an online survey drawn from a convenience sample designed to better characterize asexuality and to test predictors of asexual identity. A convenience sample of 1,146 individuals (N = 41 self-identified asexual) completed online questionnaires assessing sexual history, sexual inhibition and excitation, sexual desire, and an open-response questionnaire concerning asexual identity. Asexuals reported significantly less desire for sex with a partner, lower sexual arousability, and lower sexual excitation but did not differ consistently from non-asexuals in their sexual inhibition scores or their desire to masturbate. Content analyses supported the idea that low sexual desire is the primary feature predicting asexual identity