Quantum phase transitions and collapse of the Mott gap in the d=1+ϵd=1+\epsilon dimensional half-filled Hubbard model

We study the low-energy asymptotics of the half-filled Hubbard model with a circular Fermi surface in $d=1+\epsilon$ continuous dimensions, based on the one-loop renormalization-group (RG) method. Peculiarity of the $d=1+\epsilon$ dimensions is incorporated through the mathematica structure of the elementary particle-partcile (PP) and particle-hole (PH) loops: infrared logarithmic singularity of the PH loop is smeared for $\epsilon>0$. The RG flows indicate that a quantum phase transition (QPT) from a metallic phase to the Mott insulator phase occurs at a finite on-site Coulomb repulsion $U$ for $\epsilon>0$. We also discuss effects of randomness.Comment: 12 pages, 10 eps figure

Spin-Wave Theory of the Spiral Phase of the t-J Model

A graded H.P,realization of the SU(2|1) algebra is proposed.A spin-wave theory with a condition that the sublattice magnetization is zero is discussed.The long-range spiral phase is investigated.The spin-spin correlator is calculated.Comment: 17 page

High Temperature Superconductivity: the explanation

Soon after the discovery of the first high temperature superconductor by Georg Bednorz and Alex Mueller in 1986 the late Sir Nevill Mott answering his own question "Is there an explanation?" [Nature v 327 (1987) 185] expressed a view that the Bose-Einstein condensation (BEC) of small bipolarons, predicted by us in 1981, could be the one. Several authors then contemplated BEC of real space tightly bound pairs, but with a purely electronic mechanism of pairing rather than with the electron-phonon interaction (EPI). However, a number of other researchers criticized the bipolaron (or any real-space pairing) scenario as incompatible with some angle-resolved photoemission spectra (ARPES), with experimentally determined effective masses of carriers and unconventional symmetry of the superconducting order parameter in cuprates. Since then the controversial issue of whether the electron-phonon interaction (EPI) is crucial for high-temperature superconductivity or weak and inessential has been one of the most challenging problems of contemporary condensed matter physics. Here I outline some developments in the bipolaron theory suggesting that the true origin of high-temperature superconductivity is found in a proper combination of strong electron-electron correlations with a significant finite-range (Froehlich) EPI, and that the theory is fully compatible with the key experiments.Comment: 8 pages, 2 figures, invited comment to Physica Script

Biases in the perceived timing of perisaccadic perceptual and motor events

Subjects typically experience the temporal interval immediately following a saccade as longer than a comparable control interval. One explanation of this effect is that the brain antedates the perceptual onset of a saccade target to around the time of saccade initiation. This could explain the apparent continuity of visual perception across eye movements. Thisantedating account was tested in three experiments in which subjects made saccades of differing extents and then judged either the duration or the temporal order of key events. Postsaccadic stimuli underwent subjective temporal lengthening and had early perceived onsets. A temporally advanced awareness of saccade completion was also found, independently of antedating effects. These results provide convergent evidence supporting antedating and differentiating it from other temporal biases

Kinetic Energy, Condensation Energy, Optical Sum Rule and Pairing Mechanism in High-Tc Cuprates

The mechanism of high-Tc superconductivity is investigated with interests on the microscopic aspects of the condensation energy. The theoretical analysis is performed on the basis of the FLEX approximation which is a microscopic description of the spin-fluctuation-induced-superconductivity. Most of phase transitions in strongly correlated electron system arise from the correlation energy which is copmetitive to the kinetic energy. However, we show that the kinetic energy cooperatively induces the superconductivity in the underdoped region. This unusual decrease of kinetic energy below T_c is induced by the feedback effect. The feedback effect induces the magnetic resonance mode as well as the kink in the electronic dispersion, and alters the properties of quasi-particles, such as mass renormalization and lifetime. The crossover from BCS behavior to this unusual behavior occurs for hole dopings. On the other hand, the decrease of kinetic energy below T_c does not occur in the electron-doped region. We discuss the relation to the recent obserbation of the violation of optical sum rule

Continuous symmetry of C60 fullerene and its derivatives

Conventionally, the Ih symmetry of fullerene C60 is accepted which is supported by numerous calculations. However, this conclusion results from the consideration of the molecule electron system, of its odd electrons in particular, in a close-shell approximation without taking the electron spin into account. Passing to the open-shell approximation has lead to both the energy and the symmetry lowering up to Ci. Seemingly contradicting to a high-symmetry pattern of experimental recording, particularly concerning the molecule electronic spectra, the finding is considered in the current paper from the continuous symmetry viewpoint. Exploiting both continuous symmetry measure and continuous symmetry content, was shown that formal Ci symmetry of the molecule is by 99.99% Ih. A similar continuous symmetry analysis of the fullerene monoderivatives gives a reasonable explanation of a large variety of their optical spectra patterns within the framework of the same C1 formal symmetry exhibiting a strong stability of the C60 skeleton.Comment: 11 pages. 5 figures. 6 table

Interaction of perceptual grouping and crossmodal temporal capture in tactile apparent-motion

Previous studies have shown that in tasks requiring participants to report the direction of apparent motion, task-irrelevant mono-beeps can "capture'' visual motion perception when the beeps occur temporally close to the visual stimuli. However, the contributions of the relative timing of multimodal events and the event structure, modulating uni- and/or crossmodal perceptual grouping, remain unclear. To examine this question and extend the investigation to the tactile modality, the current experiments presented tactile two-tap apparent-motion streams, with an SOA of 400 ms between successive, left-/right-hand middle-finger taps, accompanied by task-irrelevant, non-spatial auditory stimuli. The streams were shown for 90 seconds, and participants' task was to continuously report the perceived (left-or rightward) direction of tactile motion. In Experiment 1, each tactile stimulus was paired with an auditory beep, though odd-numbered taps were paired with an asynchronous beep, with audiotactile SOAs ranging from -75 ms to 75 ms. Perceived direction of tactile motion varied systematically with audiotactile SOA, indicative of a temporal-capture effect. In Experiment 2, two audiotactile SOAs-one short (75 ms), one long (325 ms)-were compared. The long-SOA condition preserved the crossmodal event structure (so the temporal-capture dynamics should have been similar to that in Experiment 1), but both beeps now occurred temporally close to the taps on one side (even-numbered taps). The two SOAs were found to produce opposite modulations of apparent motion, indicative of an influence of crossmodal grouping. In Experiment 3, only odd-numbered, but not even-numbered, taps were paired with auditory beeps. This abolished the temporal-capture effect and, instead, a dominant percept of apparent motion from the audiotactile side to the tactile-only side was observed independently of the SOA variation. These findings suggest that asymmetric crossmodal grouping leads to an attentional modulation of apparent motion, which inhibits crossmodal temporal-capture effects

A quantum Monte Carlo study of the one-dimensional ionic Hubbard model

Quantum Monte Carlo methods are used to study a quantum phase transition in a 1D Hubbard model with a staggered ionic potential (D). Using recently formulated methods, the electronic polarization and localization are determined directly from the correlated ground state wavefunction and compared to results of previous work using exact diagonalization and Hartree-Fock. We find that the model undergoes a thermodynamic transition from a band insulator (BI) to a broken-symmetry bond ordered (BO) phase as the ratio of U/D is increased. Since it is known that at D = 0 the usual Hubbard model is a Mott insulator (MI) with no long-range order, we have searched for a second transition to this state by (i) increasing U at fixed ionic potential (D) and (ii) decreasing D at fixed U. We find no transition from the BO to MI state, and we propose that the MI state in 1D is unstable to bond ordering under the addition of any finite ionic potential. In real 1D systems the symmetric MI phase is never stable and the transition is from a symmetric BI phase to a dimerized BO phase, with a metallic point at the transition

Antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model: a non-linear sigma model approach

We describe a low-temperature approach to the two-dimensional half-filled Hubbard model which allows us to study both antiferromagnetism and single-particle properties. This approach ignores amplitude fluctuations of the antiferromagnetic (AF) order parameter and is valid below a crossover temperature $T_X$ which marks the onset of AF short-range order. Directional fluctuations (spin waves) are described by a non-linear sigma model (NL$\sigma$M) that we derive from the Hubbard model. At zero temperature and weak coupling, our results are typical of a Slater antiferromagnet. The AF gap is exponentially small; there are well-defined Bogoliubov quasi-particles (QP's) (carrying most of the spectral weight) coexisting with a high-energy incoherent excitation background. As $U$ increases, the Slater antiferromagnet progressively becomes a Mott-Heisenberg antiferromagnet. The Bogoliubov bands evolve into Mott-Hubbard bands separated by a large AF gap. A significant fraction of spectral weight is transferred from the Bogoliubov QP's to incoherent excitations. At finite temperature, there is a metal-insulator transition between a pseudogap phase at weak coupling and a Mott-Hubbard insulator at strong coupling. Finally, we point out that our results straightforwardly translate to the half-filled attractive Hubbard model, where the ${\bf q}=(\pi,\pi)$ charge and ${\bf q}=0$ pairing fluctuations combine to form an order parameter with SO(3) symmetry.Comment: Revtex4, 19 pages, 14 figures; (v2) final version as publishe