Johannes Voit

One-dimensional Fermi liquids

We review the progress in the theory of one-dimensional (ID) Fermi liquids which has occurred over the past decade. The usual Fermi liquid theory, based on a quasi-particle picture, breaks down in one dimension because of the Peierls divergence in the particle-hole bubble, producing anomalous dimensions of operators, and because of charge-spin separation. Both are related to the importance of scattering processes transferring finite momentum. A description of the low-energy properties of gapless 1D quantum systems can be based on the exactly solvable Luttinger model which incorporates these features, and whose correlation functions can be calculated. Special properties of the eigenvalue spectrum, parameterized by one renormalized velocity and one effective coupling constant per degree of freedom, fully describe the physics of this model. Other gapless 1D models share these properties in a low-energy subspace. The concept of a Luttinger liquid implies that their low-energy properties are described by an effective Luttinger model, and constitutes the universality class of these quantum systems. Once the mapping on the Luttinger model is achieved, one has an asymptotically exact solution of the 1D many-body problem. Lattice models identified as Luttinger liquids include the 1D Hubbard model off half-filling, and variants such as the t-J- or the extended Hubbard model. In addition, 1D electron-phonon systems or metals with impurities can be Luttinger liquids, as well as the edge states in the quantum Hall effect.

Charge-spin separation and the spectral properties of Luttinger liquids

We compute the spectral function p(q, ω) of the one-dimensional Luttinger model. We discuss the distinct influences of charge-spin separation and of the anomalous dimensions of the fermion operators and their evolution with correlation strength. Charge-spin separation shows up in finite spectral weight at frequencies between υσ q and υp q where υ p and υσ are the velocities of charge and spin fluctuations, while spectral weight above υp q and below -υp q is generated by the hybridization of the Fermi surface at ±k F by interactions. There are nonuniversal power-law singularities at these spectral frequencies. We discuss the consistency of recent photoemission experiments on low-dimensional conductors with a Luttinger liquid picture which then would suggest very strong long range interactions.

High-θ polyacetylene: DC conductivity between 14 mK and 300 K

Highly stretch-oriented polyacetylene (6.5:1) yields conductivities σ of typically 20 000–100 000 Ω−1cm−1 at room temperature when highly doped with iodine. Between T = 300 K and T = 14 mK, σ decreases monotonically by about a factor of 5 for fresh samples. Above 400 mK the temperature dependence for fresh samples is fitted by the SHENG formula and can be interpreted within a phenomenological model. On fresh samples, MONTGOMERY measurements of the conductivities parallel (σi) and perpendicular (σσ) to the stretching axis show a temperature independent anisotropy A=σi/σσ of about 25 indicating a common limiting mechanism for both, σi and σσ. Deliberate oxygen ageing drastically changes σ(T) and results in a temperature dependence of A.

An Exactly Solvable Kondo Problem for Interacting One-Dimensional Fermions.

The single impurity Kondo problem in the one-dimensional

Lattice twist operators and vertex operators in sine-Gordon theory in one dimension

\delta

From Brownian motion to operational risk: Statistical physics and financial markets

-potential Fermi gas is exactly solved for two sets of special coupling constants via Bethe ansatz. It is found that ferromagnetic Kondo screening does occur in one case which confirms the Furusaki-Nagaosa conjecture while in the other case it does not, which we explain in a simple physical picture. The surface energy, the low temperature specific heat and the Pauli susceptibility induced by the impurity and thereby the Kondo temperature are derived explicitly.

Dynamical correlation functions of one-dimensional superconductors and Peierls and Mott insulators

In one dimension, the exponential position operators introduced in a theory of polarization are identified with the twist operators appearing in the Lieb-Schultz-Mattis argument, and their finite-size expectation values

The Growth Dynamics Of German Business Firms

{z}_{L}^{(q)}

Exact numerical diagonalization of one-dimensional interacting electrons non-adiabatically coupled to phonons

measure the overlap between the q-fold degenerate ground state and an excited state. Insulators are characterized by

Exact boundary critical exponents and tunneling effects in integrable models for quantum wires.

{z}_{\ensuremath{\infty}}\ensuremath{\ne}0,