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arXiv:1204.0003 · Europhysics Letters (EPL)

Low-energy local density of states of the 1D Hubbard model

Stefan A. Söffing, Imke Schneider, Sebastian Eggert

Published Mar 1, 2013• 12 citations
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Abstract

We examine the local density of states (DOS) at low energies numerically and analytically for the Hubbard model in one dimension. The eigenstates represent separate spin and charge excitations with a remarkably rich structure of the local DOS in space and energy. The results predict signatures of strongly correlated excitations in the tunneling probability along finite quantum wires, such as carbon nanotubes, atomic chains or semiconductor wires in scanning tunneling spectroscopy (STS) experiments. However, the detailed signatures can only be partly explained by standard Luttinger liquid theory. In particular, we find that the effective boundary exponent can be negative in finite wires, which leads to an increase of the local DOS near the edges in contrast to the established behavior in the thermodynamic limit.

DOI
10.1209/0295-5075/101/56006

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We examine the local density of states (DOS) at low energies numerically and analytically for the Hubbard model in one dimension. The eigenstates represent separate spin and charge excitations with a remarkably rich structure of the local DOS in space and energy. The results predict signatures of strongly correlated excitations in the tunneling probability along finite quantum wires, such as carbon nanotubes, atomic chains or semiconductor wires in scanning tunneling spectroscopy (STS) experiments. However, the detailed signatures can only be partly explained by standard Luttinger liquid theory. In particular, we find that the effective boundary exponent can be negative in finite wires, which leads to an increase of the local DOS near the edges in contrast to the established behavior in the thermodynamic limit.
We calculate the finite-temperature local spectral weight (LSW) of a Luttinger liquid with an ``open'' (hard-wall) boundary. Close to the boundary the LSW exhibits characteristic oscillations indicative of spin-charge separation. The line shape of the LSW is also found to have a Fano-like asymmetry, a feature originating from the interplay between electron-electron interaction and scattering off the boundary. Our results can be used to predict how edges and impurities influence scanning tunneling microscopy (STM) of one-dimensional electron systems at low temperatures and voltage bias. Applications to STM on single-walled carbon nanotubes are discussed.
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It is now possible to create wires consisting of a single chain of atoms on an insulating substrate, with possible applications in nanoscale circuitry. However, experimental data on such systems are currently rather limited and as such a thorough theoretical investigation of such systems is required. In particular, it is useful to know to what extent the behaviour of such wires is one-dimensional - purely one-dimensional systems display Luttinger liquid behaviour, as opposed to the Fermi liquid behaviour characteristic of higher dimensional systems. However, conventional techniques in theoretical surface science are unable to provide a description of electronic correlations at the level required for one dimensional systems. The existing literature on such atomic wire systems is first reviewed. A discussion of physics in one spatial dimension follows, with a thorough introduction to both the Luttinger liquid and the analytical solutions of the Luttinger model. These concepts are then applied to a simplified model of an atomic wire system - two coupled chains of atoms, on just one of which electron-electron interactions are included. The chain which includes interactions thus represents the wire, while the non-interacting chain represents, albeit incompletely, the influence of the insulating substrate upon which the wire is embedded. Evidence for Luttinger liquid behaviour would be found in the excitation spectra and correlation functions of the system. A Fortran 90 code was written to implement the above, and both a description of the code and numerical results are presented. The results from excitations and correlation functions of the system indicate that, within the limitations of the model, Luttinger liquid behaviour may well survive. It is possible to calculate for larger and more complicated systems by use of the Density Matrix Renormalization Group (DMRG) algorithm, which relies on keeping only those states of the many particle system needed to describe the ground state and the low-energy excitations. The underlying theory of DMRG is discussed and followed with presentation of preliminary results based on a Hubbard model Hamiltonian.
We study the low-energy limit of a quarter-filled one-dimensional Mott insulator. We analytically determine the local density of states in the presence of a strong impurity potential, which is modeled by a boundary. To this end we calculate the Green function using field theoretical methods. The Fourier transform of the local density of states shows signatures of a pinning of the spin-density wave at the impurity as well as several dispersing features at frequencies above the charge gap. These features can be interpreted as propagating spin and charge degrees of freedom. Their relative strength can be attributed to the ``quasi-fermionic'' behavior of charge excitations with equal momenta. Furthermore, we discuss the effect of bound states localized at the impurity. Finally, we give an overview of the local density of states in various one-dimensional systems and discuss implications for scanning tunneling microscopy experiments.
We study the tunneling density of states (TDOS) in one-dimensional (1D) Mott insulators at energies below the charge gap. By employing nonlinear Luttinger liquid theory and density-matrix renormalization group (DMRG) simulations, we predict that in the presence of a magnetic impurity at the boundary, characteristic Fermi-edge singularity features can appear at subgap energies in the TDOS near the boundary. In contrast to the Kondo effect in a metal, these resonances are strongly asymmetric and of power-law form. The power-law exponent is universal and determined by the spinon-Kondo effect.
We study the tunneling density of states (TDOS) in one-dimensional (1D) Mott insulators at energies below the charge gap. By employing nonlinear Luttinger liquid theory and density-matrix renormalization group (DMRG) simulations, we predict that in the presence of a magnetic impurity at the boundary, characteristic Fermi-edge singularity features can appear at subgap energies in the TDOS near the boundary. In contrast to the Kondo effect in a metal, these resonances are strongly asymmetric and of power-law form. The power-law exponent is universal and determined by the spinon-Kondo effect.