Supersolid and solitonic phases in the one-dimensional extended Bose-Hubbard model

We report our findings on the quantum phase transitions in cold bosonic atoms in a one-dimensional optical lattice using the finite-size density-matrix renormalization-group method in the framework of the extended Bose-Hubbard model. We consider wide ranges of values for the filling factors and the nearest-neighbor interactions. At commensurate fillings, we obtain two different types of charge-density wave phases and a Mott insulator phase. However, departure from commensurate fillings yields the exotic supersolid phase where both the crystalline and the superfluid orders coexist. In addition, we obtain the signatures for the solitary waves and the superfluid phase.

Quantum phase analysis of 1D superconducting quantum dot lattice using extended Bose-Hubbard model

We have obtained the quantum phase diagram of a one-dimensional superconducting quantum dot lattice using the extended Bose-Hubbard model for different commensurabilities. We describe the nature of different quantum phases at the charge degeneracy point. We find a direct phase transition from the Mott insulating phase to the superconducting phase for integer band fillings of Cooper pairs. We predict explicitly the presence of two kinds of repulsive Luttinger liquid phases, besides the charge density wave and superconducting phases for half-integer band fillings. We also predict that extended range interactions are necessary to obtain the correct phase boundary of a one-dimensional interacting Cooper system. We have used the density matrix renormalization group method and Abelian bosonization to study our system.

Low-lying states of transverse substituted trans-polyacetylene and trans-polyacetylene: A comparative DMRG study

The density-matrix renormalization group (DMRG) method is used for a comparative study of low-lying excitations in trans-polyacetylene (t-PA) and transversely substituted t-PA (TS-t-PA). We have employed the Pariser-Parr-Pople model Hamiltonian which incorporates long-range electronic correlations to model these systems. We find some fundamental differences in the excited states of the t-PA and TS-t-PA. We find that the lowest two-photon allowed excited state in TS-t-PA is not made up of two triplet excitons and the gap to this state is nonzero even for undimerized chains in the thermodynamic limit. Contrary to earlier results for the Hubbard model, we find that the lowest two-photon state is always below the first optically allowed state in all the systems studied here making TS-t-PA systems only weakly fluorescent materials. Nonresonant tumbling averaged linear and third harmonic generation optic coefficients of TS-t-PA systems are also much smaller than that of t-PA.

Polymer drift in a solvent by force acting on one polymer end

We investigate the effect of hydrodynamic interactions on the non-equilibrium drift dynamics of an ideal flexible polymer pulled by a constant force applied at one polymer end using the perturbation theory and the renormalization group method. For moderate force, if the polymer elongation is small, the hydrodynamic interactions are not screened and the velocity and the longitudinal elongation of the polymer are computed using the renormalization group method. Both the velocity and elongation are nonlinear functions of the driving force in this regime. For large elongation we found two regimes. For large force but finite chain length L the hydrodynamic interactions are screened. For large chain lengths and a finite force the hydrodynamic interactions are only partially screened, which in three dimensions results in unusual logarithmic corrections to the velocity and the longitudinal elongation.

Tendency toward crossover of the effective susceptibility exponent from its doubled Ising value to its doubled mean-field value near a double critical point

The critical behavior of osmotic susceptibility in an aqueous electrolyte mixture 1-propanol (1P)+water (W)+potassium chloride is reported. This mixture exhibits re-entrant phase transitions and has a nearly parabolic critical line with its apex representing a double critical point (DCP). The behavior of the susceptibility exponent is deduced from static light-scattering measurements, on approaching the lower critical solution temperatures (TL’s) along different experimental paths (by varying t) in the one-phase region. The light-scattering data analysis substantiates the existence of a nonmonotonic crossover behavior of the susceptibility exponent in this mixture. For the TL far away from the DCP, the effective susceptibility exponent γeff as a function of t displays a nonmonotonic crossover from its single limit three-dimensional (3D)-Ising value ( ∼ 1.24) toward its mean-field value with increase in t. While for that closest to the DCP, γeff displays a sharp, nonmonotonic crossover from its nearly doubled 3D-Ising value toward its nearly doubled mean-field value with increase in t. The renormalized Ising regime extends over a relatively larger t range for the TL closest to the DCP, and a trend toward shrinkage in the renormalized Ising regime is observed as TL shifts away from the DCP. Nevertheless, the crossover to the mean-field limit extends well beyond t>10−2 for the TL’s studied. The observed crossover behavior is attributed to the presence of strong ion-induced clustering in this mixture, as revealed by various structure probing techniques. As far as the critical behavior in complex or associating mixtures with special critical points (like the DCP) is concerned, our results indicate that the influence of the DCP on the critical behavior must be taken into account not only on the renormalization of the critical exponent but also on the range of the Ising regime, which can shrink with decrease in the influence of the DCP and with the extent of structuring in the system. The utility of the field variable tUL in analyzing re-entrant phase transitions is demonstrated. The effective susceptibility exponent as a function of tUL displays a nonmonotonic crossover from its asymptotic 3D-Ising value toward a value slightly lower than its nonasymptotic mean-field value of 1. This behavior in the nonasymptotic, high tUL region is interpreted in terms of the possibility of a nonmonotonic crossover to the mean-field value from lower values, as foreseen earlier in micellar systems.

Quantum phase transition in capacitively coupled double quantum dots

We investigate two equivalent, capacitively coupled semiconducting quantum dots, each coupled to its own lead, in a regime where there are two electrons on the double dot. With increasing interdot coupling, a rich range of behavior is uncovered: first a crossover from spin- to charge-Kondo physics, via an intermediate SU(4) state with entangled spin and charge degrees of freedom, followed by a quantum phase transition of Kosterlitz-Thouless type to a non-Fermi-liquid "charge-ordered" phase with finite residual entropy and anomalous transport properties. Physical arguments and numerical renormalization group methods are employed to obtain a detailed understanding of the problem.

Dynamics of capacitively coupled double quantum dots

We consider a double dot system of equivalent, capacitively coupled semiconducting quantum dots, each coupled to its own lead, in a regime where there are two electrons on the double dot. Employing the numerical renormalization group, we focus here on single-particle dynamics and the zero-bias conductance, considering in particular the rich range of behaviour arising as the interdot coupling is progressively increased through the strong-coupling (SC) phase, from the spin-Kondo regime, across the SU(4) point to the charge-Kondo regime, and then towards and through the quantum phase transition to a charge-ordered ( CO) phase. We first consider the two-self-energy description required to describe the broken symmetry CO phase, and implications thereof for the non-Fermi liquid nature of this phase. Numerical results for single-particle dynamics on all frequency scales are then considered, with particular emphasis on universality and scaling of low-energy dynamics throughout the SC phase. The role of symmetry breaking perturbations is also briefly discussed.

Double time window targeting technique: Real-time DMRG dynamics in the Pariser-Parr-Pople model

We present a generalized adaptive time-dependent density matrix renormalization-group (DMRG) scheme, called the double time window targeting (DTWT) technique, which gives accurate results with nominal computational resources, within reasonable computational time. This procedure originates from the amalgamation of the features of pace keeping DMRG algorithm, first proposed by Luo et al. [Phys. Rev. Lett. 91, 049701 (2003)] and the time-step targeting algorithm by Feiguin and White [Phys. Rev. B 72, 020404 (2005)]. Using the DTWT technique, we study the phenomena of spin-charge separation in conjugated polymers (materials for molecular electronics an spintronics), which have long-range electron-electron interactions and belong to the class of strongly correlated low-dimensional many-body systems. The issue of real-time dynamics within the Pariser-Parr-Pople (PPP) model which includes long-range electron correlations has not been addressed in the literature so far. The present study on PPP chains has revealed that, (i) long-range electron correlations enable both the charge and spin degree of freedom of the electron, to propagate faster in the PPP model compared to Hubbard model, (ii) for standard parameters of the PPP model as applied to conjugated polymers, the charge velocity is almost twice that of the spin velocity, and (iii) the simplistic interpretation of long-range correlations by merely renormalizing the U value of the Hubbard model fails to explain the dynamics of doped holes/electrons in the PPP model.

An electron paramagnetic resonance study of Pr0.6Ca0.4MnO3 across the charge-ordering transition

We report the first electron paramagnetic resonance studies of single crystals and powders of Pr0.6Ca0.4MnO3 in the 300-4.2 K range, covering the charge-ordering transition (Tco) at ~240 K and antiferromagnetic transition (TN) at ~170 K. The asymmetry parameter for the Dysonian single-crystal spectra shows an anomalous increase at Tco. Below Tco the g-value increases continuously, suggesting a gradual strengthening of the orbital ordering. The linewidth undergoes a sudden increase at Tco and continues to increase down to TN. The intensity increases as the temperature is decreased until Tco is reached, due to the renormalization of the magnetic susceptibility arising from the build-up of ferromagnetic correlations.

Isobaric electrical resistance along the critical line in nickel: An experimental test of universality

High-precision measurement of the electrical resistance of nickel along its critical line, a first attempt of this kind, as a function of pressure to 47.5 kbar is reported. Our analysis yields the values of the critical exponents α=α’=-0.115±0.005 and the amplitude ratios ‖A/A’‖=1.17±0.07 and ‖D/D’‖=1.2±0.1. These values are in close agreement with those predicted by renormalization-group (RG) theory. Moreover, this investigation provides an unambiguous experimental verification to one of the key consequences of RG theory that the critical exponents and amplitudes ratios are insensitive to pressure variation in nickel, a Heisenberg ferromagnet.

Ordering near the percolation threshold in models of two-dimensional interacting bosons with quenched dilution

Randomly diluted quantum boson and spin models in two dimensions combine the physics of classical percolation with the well-known dimensionality dependence of ordering in quantum lattice models. This combination is rather subtle for models that order in two dimensions but have no true order in one dimension, as the percolation cluster near threshold is a fractal of dimension between 1 and 2: two experimentally relevant examples are the O(2) quantum rotor and the Heisenberg antiferromagnet. We study two analytic descriptions of the O(2) quantum rotor near the percolation threshold. First a spin-wave expansion is shown to predict long-ranged order, but there are statistically rare points on the cluster that violate the standard assumptions of spin-wave theory. A real-space renormalization group (RSRG) approach is then used to understand how these rare points modify ordering of the O(2) rotor. A new class of fixed points of the RSRG equations for disordered one-dimensional bosons is identified and shown to support the existence of long-range order on the percolation backbone in two dimensions. These results are relevant to experiments on bosons in optical lattices and superconducting arrays, and also (qualitatively) for the diluted Heisenberg antiferromagnet La-2(Zn,Mg)(x)Cu1-xO4.

Mooij correlation in disordered metals

We point out that the Mooij correlation follows naturally from a dynamically disordered tight-binding Hamiltonian with random modulations of both the diagonal and the off-diagonal matrix elements which are known to act in opposition. The dynamic disorder is treated exactly while the static disorder is incorporated approximately as an effective additional time-dependent disorder affecting the diffusive electron. Such a time translation of static disorder is known to manifest itself in certain limits as a renormalization of the diffusion coefficient. The calculated conductivity exhibits the Mooij correlation at high temperatures, where quantum coherence associated with the static disorder can be ignored.

Spatially dependent correlation functions in the Anderson model

We report results from a first principles calculation of spatially dependent correlation functions around a magnetic impurity in metals described by the nondegenerate Anderson model. Our computations are based on a combination of perturbative scaling theory and numerical renormalization group methods. Results for the conduction election charge density around the impurity and correlation functions involving the conduction electron and impurity charge and spin densities will be presented. The behavior in various regimes including the mixed valent regime will be explored.

Metal-Insulator Transition in the Hubbard Model on a Triangular Lattice

We discuss the results of an extensive mean-field investigation of the half-filled Hubbard model on a triangular lattice at zero temperature. At intermediate U we find a first-order metal-insulator transition from an incommensurate spiral magnetic metal to a semiconducting state with a commensurate linear spin density wave ordering stabilized by the competition between the kinetic energy and the frustrated nature of the magnetic interaction. At large U the ground state is that of a classical triangular antiferromagnet within our approximation. In the incommensurate spiral metallic phase the Fermi surface has parts in which the wave function renormalization Z is extremely small. The evolution of the Fermi surface and the broadening of the quasi-particle band along with the variation of the plasma frequency and a charge stiffness constant with U/t are discussed.

Infrared divergences and confinement in massive (2+1)-dimensional QED

In (2+1)-dimensional quantum electrodynamics with massless photons and massive matter fields, it is shown that the mass renormalization of the latter is infrared divergent at one loop. This result remains unchanged at two loops. A simple argument based on a similar divergence of the Coulomb potential leads us to conjecture that charged states are not observable in this model. This argument holds in 1+1 dimensions also.