Quantum lattice dynamical effects on the single-particle excitations in 1D Mott and Peierls insulators

As a generic model describing quasi-one-dimensional Mott and Peierls insulators, we investigate the Holstein-Hubbard model for half-filled bands using numerical techniques. Combining Lanczos diagonalization with Chebyshev moment expansion we calculate exactly the photoemission and inverse photoemission spectra and use these to establish the phase diagram of the model. While polaronic features emerge only at strong electron-phonon couplings, pronounced phonon signatures, such as multi-quanta band states, can be found in the Mott insulating regime as well. In order to corroborate the Mott to Peierls transition scenario, we determine the spin and charge excitation gaps by a finite-size scaling analysis based on density-matrix renormalization group calculations.Comment: 5 pages, 5 figure

Mott-Peierls Transition in the extended Peierls-Hubbard model

The one-dimensional extended Peierls-Hubbard model is studied at several band fillings using the density matrix renormalization group method. Results show that the ground state evolves from a Mott-Peierls insulator with a correlation gap at half-filling to a soliton lattice with a small band gap away from half-filling. It is also confirmed that the ground state of the Peierls-Hubbard model undergoes a transition to a metallic state at finite doping. These results show that electronic correlations effects should be taken into account in theoretical studies of doped polyacetylene. They also show that a Mott-Peierls theory could explain the insulator-metal transition observed in this material.Comment: 4 pages with 3 embedded eps figure

Density-matrix renormalisation group approach to quantum impurity problems

A dynamic density-matrix renormalisation group approach to the spectral properties of quantum impurity problems is presented. The method is demonstrated on the spectral density of the flat-band symmetric single-impurity Anderson model. We show that this approach provides the impurity spectral density for all frequencies and coupling strengths. In particular, Hubbard satellites at high energy can be obtained with a good resolution. The main difficulties are the necessary discretisation of the host band hybridised with the impurity and the resolution of sharp spectral features such as the Abrikosov-Suhl resonance.Comment: 16 pages, 6 figures, submitted to Journal of Physics: Condensed Matte

Induced local spin-singlet amplitude and pseudogap in high TcT_{c} cuprates

In this paper we show that local spin-singlet amplitude with d-wave symmetry, , can be induced by short-range spin correlations even in the absence of pairing interactions. Fluctuation theory is formulated to make connection between pseudogap temperature $T^{*}$, pseudogap size $\Delta_{pg}$ and . In the present scenario for the pseudogap, the normal state pseudogap is caused by the induced local spin-singlet amplitude due to short-range spin correlations, which compete in the low energy sector with superconducting correlations to make $T_{c}$ go to zero near half-filling. Calculated $T^{*}$ falls from a high value onto the $T_{c}$ line and closely follows mean-field N\'{e}el temperature $T_{N}^{MF}$. The calculated $\Delta_{pg}$ is in good agreement with experimental results. We propose an experiment in which the present scenario can be critically tested.Comment: 5 pages, 3 figure

Continuous-Time Quantum Monte Carlo Algorithm for the Lattice Polaron

An efficient continuous-time path-integral Quantum Monte Carlo algorithm for the lattice polaron is presented. It is based on Feynman's integration of phonons and subsequent simulation of the resulting single-particle self-interacting system. The method is free from the finite-size and finite-time-step errors and works in any dimensionality and for any range of electron-phonon interaction. The ground-state energy and effective mass of the polaron are calculated for several models. The polaron spectrum can be measured directly by Monte Carlo, which is of general interest.Comment: 5 pages, 4 figures, published versio

Ground-state dispersion and density of states from path-integral Monte Carlo. Application to the lattice polaron

A formula is derived that relates the ground-state dispersion of a many-body system with the end-to-end distribution of paths with open boundary conditions in imaginary time. The formula does not involve the energy estimator. It allows direct measurement of the ground-state dispersion by quantum Monte Carlo methods without analytical continuation or auxiliary fitting. The formula is applied to the lattice polaron problem. The exact polaron spectrum and density of states are calculated for several models in one, two, and three dimensions. In the adiabatic regime of the Holstein model, the polaron density of states deviates spectacularly from the free-particle shape.Comment: 8 pages, 9 figure

Excitation Spectrum of the Holstein Model

In this paper the polaron problem for the Holstein model is studied in the weak coupling limit. We use second order perturbation theory to construct renormalized electron and phonons. Eigenstates of the Hamiltonian are labelled and the excitation spectrum is constructed.Comment: 4 pages, revtex, 1 figures, more stuff at http://www.mpipks-dresden.mpg.de/~robin/robin.htm

Excitons in one-dimensional Mott insulators

We employ dynamical density-matrix renormalization group (DDMRG) and field-theory methods to determine the frequency-dependent optical conductivity in one-dimensional extended, half-filled Hubbard models. The field-theory approach is applicable to the regime of `small' Mott gaps which is the most difficult to access by DDMRG. For very large Mott gaps the DDMRG recovers analytical results obtained previously by means of strong-coupling techniques. We focus on exciton formation at energies below the onset of the absorption continuum. As a consequence of spin-charge separation, these Mott-Hubbard excitons are bound states of spinless, charged excitations (`holon-antiholon' pairs). We also determine exciton binding energies and sizes. In contrast to simple band insulators, we observe that excitons exist in the Mott-insulating phase only for a sufficiently strong intersite Coulomb repulsion. Furthermore, our results show that the exciton binding energy and size are not related in a simple way to the strength of the Coulomb interaction.Comment: 15 pages, 6 eps figures, corrected typos in labels of figures 4,5, and

The density-matrix renormalization group

The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. This algorithm has achieved unprecedented precision in the description of one-dimensional quantum systems. It has therefore quickly acquired the status of method of choice for numerical studies of one-dimensional quantum systems. Its applications to the calculation of static, dynamic and thermodynamic quantities in such systems are reviewed. The potential of DMRG applications in the fields of two-dimensional quantum systems, quantum chemistry, three-dimensional small grains, nuclear physics, equilibrium and non-equilibrium statistical physics, and time-dependent phenomena is discussed. This review also considers the theoretical foundations of the method, examining its relationship to matrix-product states and the quantum information content of the density matrices generated by DMRG.Comment: accepted by Rev. Mod. Phys. in July 2004; scheduled to appear in the January 2005 issu