DMRG analysis of the SDW-CDW crossover region in the 1D half-filled Hubbard-Holstein model

In order to clarify the physics of the crossover from a spin-density-wave (SDW) Mott insulator to a charge-density-wave (CDW) Peierls insulator in one-dimensional (1D) systems, we investigate the Hubbard-Holstein Hamiltonian at half filling within a density matrix renormalisation group (DMRG) approach. Determining the spin and charge correlation exponents, the momentum distribution function, and various excitation gaps, we confirm that an intervening metallic phase expands the SDW-CDW transition in the weak-coupling regime.Comment: revised versio

Metal-insulator transition in the Edwards model

To understand how charge transport is affected by a background medium and vice versa we study a two-channel transport model which captures this interplay via a novel, effective fermion-boson coupling. By means of (dynamical) DMRG we prove that this model exhibits a metal-insulator transition at half-filling, where the metal typifies a repulsive Luttinger liquid and the insulator constitutes a charge density wave. The quantum phase transition point is determined consistently from the calculated photoemission spectra, the scaling of the Luttinger liquid exponent, the charge excitation gap, and the entanglement entropy.Comment: 4 pages, 3 figures, contributions to SCES 201

Face Pose Estimation From Video Sequence Using Dynamic Bayesian Network.

This paper describes a technique to estimate human face pose from colour video sequence using Dynamic Bayesian Network(DBN). As face and facial features trackers usually track eyes, pupils, mouth corners and skin region(face), our proposed method utilizes merely three of these features – pupils, mouth centre and skin region – to compute the evidence for DBN inference

A Green's function decoupling scheme for the Edwards fermion-boson model

Holes in a Mott insulator are represented by spinless fermions in the fermion-boson model introduced by Edwards. Although the physically interesting regime is for low to moderate fermion density the model has interesting properties over the whole density range. It has previously been studied at half-filling in the one-dimensional (1D) case by numerical methods, in particular exact diagonalization and density matrix renormalization group (DMRG). In the present study the one-particle Green's function is calculated analytically by means of a decoupling scheme for the equations of motion, valid for arbitrary density in 1D, 2D and 3D with fairly large boson energy and zero boson relaxation parameter. The Green's function is used to compute some ground state properties, and the one-fermion spectral function, for fermion densities n=0.1, 0.5 and 0.9 in the 1D case. The results are generally in good agreement with numerical results obtained by DMRG and dynamical DMRG and new light is shed on the nature of the ground state at different fillings. The Green's function approximation is sufficiently successful in 1D to justify future application to the 2D and 3D cases.Comment: 19 pages, 7 figures, final version with updated reference

Luttinger parameters and momentum distribution function for the half-filled spinless fermion Holstein model: A DMRG approach

We reexamine the nature of the metallic phase of the one-dimensional half-filled Holstein model of spinless fermions. To this end we determine the Tomonaga-Luttinger-liquid correlation parameter $K_\rho$ by large-scale density-matrix renormalisation-group (DMRG) calculations, exploiting (i) the leading-order scaling relations between the ground-state energy and the single-particle excitation gap and (ii) the static charge structure factor in the long-wavelength limit. While both approaches give almost identical results for intermediate-to-large phonon frequencies, we find contrasting behaviour in the adiabatic regime: (i) $K_\rho>1$ (attractive) versus (ii) $K_\rho<1$ (repulsive). The latter result for the correlation exponent is corroborated by data obtained for the momentum distribution function $n(k)$, which puts the existence of an attractive metallic state in the spinless fermion Holstein model into question. We conclude that the scaling relation must be modified in the presence of electron-phonon interactions with noticeable retardation.Comment: 6 pages, 5 figures, revised versio

Dynamic properties of the one-dimensional Bose-Hubbard model

We use the density-matrix renormalization group method to investigate ground-state and dynamic properties of the one-dimensional Bose-Hubbard model, the effective model of ultracold bosonic atoms in an optical lattice. For fixed maximum site occupancy $n_b=5$, we calculate the phase boundaries between the Mott insulator and the `superfluid' phase for the lowest two Mott lobes. We extract the Tomonaga-Luttinger parameter from the density-density correlation function and determine accurately the critical interaction strength for the Mott transition. For both phases, we study the momentum distribution function in the homogeneous system, and the particle distribution and quasi-momentum distribution functions in a parabolic trap. With our zero-temperature method we determine the photoemission spectra in the Mott insulator and in the `superfluid' phase of the one-dimensional Bose-Hubbard model. In the insulator, the Mott gap separates the quasi-particle and quasi-hole dispersions. In the `superfluid' phase the spectral weight is concentrated around zero momentum.Comment: 6 pages, 7 figure

Strong coupling expansion for the Bose-Hubbard and the Jaynes-Cummings lattice model

A strong coupling expansion, based on the Kato-Bloch perturbation theory, which has recently been proposed by Eckardt et al. [Phys. Rev. B 79, 195131] and Teichmann et al. [Phys. Rev. B 79, 224515] is implemented in order to study various aspects of the Bose-Hubbard and the Jaynes-Cummings lattice model. The approach, which allows to generate numerically all diagrams up to a desired order in the interaction strength is generalized for disordered systems and for the Jaynes-Cummings lattice model. Results for the Bose-Hubbard and the Jaynes-Cummings lattice model will be presented and compared with results from VCA and DMRG. Our focus will be on the Mott insulator to superfluid transition.Comment: 29 pages, 21 figure

Magnetic Properties of the Second Mott Lobe in Pairing Hamiltonians

We explore the Mott insulating state of single-band bosonic pairing Hamiltonians using analytical approaches and large scale density matrix renormalization group calculations. We focus on the second Mott lobe which exhibits a magnetic quantum phase transition in the Ising universality class. We use this feature to discuss the behavior of a range of physical observables within the framework of the 1D quantum Ising model and the strongly anisotropic Heisenberg model. This includes the properties of local expectation values and correlation functions both at and away from criticality. Depending on the microscopic interactions it is possible to achieve either antiferromagnetic or ferromagnetic exchange interactions and we highlight the possibility of observing the E8 mass spectrum for the critical Ising model in a longitudinal magnetic field.Comment: 14 pages, 15 figure

Characterization of Mott-insulating and superfluid phases in the one-dimensional Bose--Hubbard model

We use strong-coupling perturbation theory, the variational cluster approach (VCA), and the dynamical density-matrix renormalization group (DDMRG) method to investigate static and dynamical properties of the one-dimensional Bose--Hubbard model in both the Mott-insulating and superfluid phases. From the von Neumann entanglement entropy we determine the central charge and the transition points for the first two Mott lobes. Our DMRG results for the ground-state energy, momentum distribution function, boson correlation function decay, Mott gap, and single particle-spectral function are reproduced very well by the strong-coupling expansion to fifth order, and by VCA with clusters up to 12 sites as long as the ratio between the hopping amplitude and on-site repulsion, t/U, is smaller than 0.15 and 0.25, respectively. In addition, in the superfluid phase VCA captures well the ground-state energy and the sound velocity of the linear phonon modes. This comparison provides an authoritative estimate for the range of applicability of these methods. In strong-coupling theory for the Mott phase, the dynamical structure factor is obtained from the solution of an effective single-particle problem with an attractive potential. The resulting resonances show up as double-peak structure close to the Brillouin zone boundary. These high-energy features also appear in the superfluid phase which is characterized by a pronounced phonon mode at small momenta and energies, as predicted by Bogoliubov and field theory. In one dimension, there are no traces of an amplitude mode in the dynamical single-particle and two-particle correlation functions.Comment: 15 pages, 12 figure

Local spectral properties of Luttinger liquids: scaling versus nonuniversal energy scales

Motivated by recent scanning tunneling and photoemission spectroscopy measurements on self-organized gold chains on a germanium surface we reinvestigate the local single-particle spectral properties of Luttinger liquids. In the first part we use the bosonization approach to exactly compute the local spectral function of a simplified field theoretical low-energy model and take a closer look at scaling properties as a function of the ratio of energy and temperature. Translational invariant Luttinger liquids as well as those with an open boundary (cut chain geometry) are considered. We explicitly show that the scaling functions of both setups have the same analytic form. The scaling behavior suggests a variety of consistency checks which can be performed on measured data to experimentally verify Luttinger liquid behavior. In a second part we approximately compute the local spectral function of a microscopic lattice model---the extended Hubbard model---close to an open boundary using the functional renormalization group. We show that as a function of energy and temperature it follows the field theoretical prediction in the low-energy regime and point out the importance of nonuniversal energy scales inherent to any microscopic model. The spatial dependence of this spectral function is characterized by oscillatory behavior and an envelope function which follows a power law both in accordance with the field theoretical continuum model. Interestingly, for the lattice model we find a phase shift which is proportional to the two-particle interaction and not accounted for in the standard bosonization approach to Luttinger liquids with an open boundary. We briefly comment on the effects of several one-dimensional branches cutting the Fermi energy and Rashba spin-orbit interaction.Comment: 19 pages, 5 figures, version as accepted for publication in J. Phys.:Condensed Matte