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

Random dispersion approximation for the Hubbard model

We use the Random Dispersion Approximation (RDA) to study the Mott-Hubbard transition in the Hubbard model at half band filling. The RDA becomes exact for the Hubbard model in infinite dimensions. We implement the RDA on finite chains and employ the Lanczos exact diagonalization method in real space to calculate the ground-state energy, the average double occupancy, the charge gap, the momentum distribution, and the quasi-particle weight. We find a satisfactory agreement with perturbative results in the weak- and strong-coupling limits. A straightforward extrapolation of the RDA data for $L\leq 14$ lattice results in a continuous Mott-Hubbard transition at $U_{\rm c}\approx W$. We discuss the significance of a possible signature of a coexistence region between insulating and metallic ground states in the RDA that would correspond to the scenario of a discontinuous Mott-Hubbard transition as found in numerical investigations of the Dynamical Mean-Field Theory for the Hubbard model.Comment: 10 pages, 11 figure

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

Tomonaga-Luttinger parameters for doped Mott insulators

The Tomonaga--Luttinger parameter $K_{\rho}$ determines the critical behavior in quasi one-dimensional correlated electron systems, e.g., the exponent $\alpha$ for the density of states near the Fermi energy. We use the numerical density-matrix renormalization group method to calculate $K_{\rho}$ from the slope of the density-density correlation function in momentum space at zero wave vector. We check the accuracy of our new approach against exact results for the Hubbard and XXZ Heisenberg models. We determine $K_{\rho}$ in the phase diagram of the extended Hubbard model at quarter filling, $n_{\rm c}=1/2$, and confirm the bosonization results $K_{\rho}=n_{\rm c}^2=1/4$ on the critical line and $K_{\rho}^{\rm CDW}=n_{\rm c}^2/2=1/8$ at infinitesimal doping of the charge-density-wave (CDW) insulator for all interaction strengths. The doped CDW insulator exhibits exponents $\alpha>1$ only for small doping and strong correlations.Comment: 7 pages, 4 figure

Peierls to superfluid crossover in the one-dimensional, quarter-filled Holstein model

We use continuous-time quantum Monte Carlo simulations to study retardation effects in the metallic, quarter-filled Holstein model in one dimension. Based on results which include the one- and two-particle spectral functions as well as the optical conductivity, we conclude that with increasing phonon frequency the ground state evolves from one with dominant diagonal order---2k_F charge correlations---to one with dominant off-diagonal fluctuations, namely s-wave pairing correlations. In the parameter range of this crossover, our numerical results support the existence of a spin gap for all phonon frequencies. The crossover can hence be interpreted in terms of preformed pairs corresponding to bipolarons, which are essentially localised in the Peierls phase, and "condense" with increasing phonon frequency to generate dominant pairing correlations.Comment: 11 pages, 5 figure

Phase separation in the Edwards model

The nature of charge transport within a correlated background medium can be described by spinless fermions coupled to bosons in the model introduced by Edwards. Combining numerical density matrix renormalization group and analytical projector-based renormalization methods we explore the ground-state phase diagram of the Edwards model in one dimension. Below a critical boson frequency any long-range order disappears and the system becomes metallic. If the charge carriers are coupled to slow quantum bosons the Tomonaga-Luttinger liquid is attractive and finally makes room for a phase separated state, just as in the t-J model. The phase boundary separating repulsive from the attractive Tomonaga-Luttinger liquid is determined from long-wavelength charge correlations, whereas fermion segregation is indicated by a vanishing inverse compressibility. On approaching phase separation the photoemission spectra develop strong anomalies.Comment: 6 pages, 5 figures, final versio

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

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

Anharmonicity in one-dimensional electron-phonon system

We investigate the effect of anharmonicity on the one-dimensional half-filled Holstein model by using the determinant quantum Monte Carlo method. By calculating the order parameters we find that with and without anharmonicity there is always an transition from a disorder phase to a dimerized phase. Moreover, in the dimerized phase a lattice dimerization and a charge density wave coexist. The anharmonicity represented by the quartic term suppresses the dimerization as well as the charge density wave, while a double-well potential favors the dimerization. In addition, by calculating the correlation exponents we show that the disorder phase is metallic with gapless charge excitations and gapful spin excitations while in the dimerized phase both excitations are gapful.Comment: 5 page

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