Plenarvorträge - DPG-Tagungen

Tiefe Temperaturen Mittwoch
2003
TT 24.12 Mi 14:30 Poster A
Hubbard model in a magnetic field at weak coupling —
•Carsten L. Knecht and P.G.J. van Dongen — Institut für
Physik, Johannes Gutenberg-Universität, Staudinger Weg 7, 55099
Mainz, Germany
The phase diagram of the half-filled Hubbard model is studied at weak
coupling in two spatial dimensions. A homogeneous magnetization in
the z-direction and a staggered magnetization in the x-direction are assumed.
We apply perturbation theory at fixed order parameter (PTFO)
to this system. The results are compared with the well know Hartree-Fock
solutions that usually overestimate the order parameters. This calculation
is also relevant for superconductivity in the doped two-dimensional
negative-U Hubbard model.
TT 24.13 Mi 14:30 Poster A
Self-energy-functional approach: New results and developments
— •Michael Potthoff — Institut für Theoretische Physik und Astrophysik,
Universität Würzburg
The self-energy-functional approach [1-3] is a general variational framework
to construct non-perturbative and thermodynamically consistent
approximations for lattice models of correlated electrons. The main idea
is to shift the problem to a more simple reference system with the same
(two-particle) interaction which is exactly solved for different one-particle
parameters. The parameters are fixed by evaluation of a fundamental variational
principle for the self-energy.
This contribution gives an overview over the recent developments in
the extension of the approach to Bose systems, two-particle excitations or
disordered systems and discusses efficient numerical methods to evaluate
the variational principle.
[1] M.P., EPJB 32, 429 (2003)
[2] M.P., M. Aichhorn and C. Dahnken, PRL 91, 206402 (2003)
[3] M.P., EPJB in press, cond-mat/0306278
TT 24.14 Mi 14:30 Poster A
Crossover from Non-equilibrium to Equilibrium Behavior in the
Time–DependentKondo Model — •Stefan Kehrein and Dmitry
Lobaskin — Insitut für Physik – Elektronische Korrelationen und Magnetismus,
Universität Augsburg
We investigate the equilibration of a Kondo model that is initially
prepared in a non–equilibrium state towards its equilibrium behavior
for large times. Such initial non–equilibrium states can e.g. be realized
in quantum dot experiments with time–dependent gate voltages or
in rf SQUIDS. We evaluate the spin–spin correlation function at the
Toulouse point of the Kondo model exactly and show that there is a
smooth crossover between non–equilibrium and equilibrium behavior as
the non–equilibrium initial state decays as a function of the waiting time.
In particular, we demonstrate that the decaying non–equilibrium state
cannot be thought of as an equilibrium state with an effective temperature
that depends on the waiting time.
TT 24.15 Mi 14:30 Poster A
Finite temperature Drude weight of strongly correlated 1d systems
— •Stefan Glocke and Andreas Klümper — Universität
Wuppertal, Theoretische Physik, Gauß-Straße 20
We present results for the Drude weight Ds of the spin conductivity
σ of the integrable spin-1/2 XXZ chain at arbitrary temperature (σ =
electrical conductivity in the spinless fermion language of the model). The
results are obtained by a combination of linear response theory (Kubo
formula) and solution techniques of Bethe ansatz type. Unlike the case
of thermal conductivity, the state of investigation of the spin conductivity
of the XXZ chain is less complete if not controversial. The reason
for this lies in the non-conservation of the spin (charge) current. Despite
this, there is a delta-function peak at zero frequency in the dynamical
conductivity σ(ω) = Ds · δ(ω) + σreg(ω). The controversies of [1],[2]
and more recent treatments arise about the anisotropy (interaction) and
temperature dependence of Ds. Some of the controversies are resolved by
the observation of a strong variation of the energy level curvatures even
within a microcanonical ensemble between “very similar states”.
[1] B.N. Narozhny, A.J. Millis, N. Andrei: Phys. Rev. B 58, R2921 (1998)
[1] X. Zotos: Phys. Rev. Lett. 82, 1764 (1999)
TT 24.16 Mi 14:30 Poster A
General susceptibilities of highly correlated electron systems
from a local point of view — •Sebastian Schmitt and Norbert
Grewe — Institut für Festkörperphysik, Hochschulstraße 6, 64289
Darmstadt
Starting from a cumulant expansion in terms of the transfer between
lattice sites in the presence of large local Coulomb matrix elements,
Bethe-Salpeter equations are derived. Using only local particle-hole or
particle-particle irreducible vertices, as in the dynamical mean field theory,
general susceptibilities can be approximated. Employing a decoupling
scheme for the energy summations, a typical Stoner-form is obtained,
where the local interaction part is explicitly known.
In the case of the Hubbard model the magnetic susceptibility is studied
in detail.
TT 24.17 Mi 14:30 Poster A
Charge Fluctuations in the t-U-V1-V2 Model — •Satoshi Ejima 1 ,
Florian Gebhard 1 , Satoshi Nishimoto 1 , and Yukinori Ohta 2 —
1 Fachbereich Physik, Philipps-Universität Marburg, 35032 Marburg —
2 Department of Physics, Chiba University, Chiba 263-8522, Japan
Recently, charge dynamics has attracted much interest in the
transition-metal oxide PrBa2Cu3O7 and in the organic conductor
(TYMTSF)2. In the low-energy physics of these materials, charge
fluctuations play a crucial role, due to the frustration of the long-range
Coulomb interactions.
The minimal model for these systems is the one-dimensional
quarter-filled Hubbard model with nearest-neighbor (V1) and nextnearest-neighbor
(V2) Coulomb interactions. We investigate the ground
state and some excited states using the (dynamical) density-matrix
renormalization group technique. We present an accurate phase diagram
and discuss the possible emergence of a metallic (or superconducting)
phase induced by charge fluctuations. Moreover, we compare our
single-chain results with calculations for double-chain systems such as
PrBa2Cu4O8 [1].
[1] S. Nishimoto and Y. Ohta, cond-mat/0305610
TT 24.18 Mi 14:30 Poster A
Analytical and numerical treatment of the Mott–Hubbard
insulator in infinite dimensions — •Satoshi Nishimoto 1 ,
Satoshi Ejima 1 , Florian Gebhard 1 , Eva Kalinowski 1 , Reinhard
M. Noack 1 , and Eric Jeckelmann 2 — 1 Fachbereich Physik,
Philipps-Universität Marburg, 35032 Marburg — 2 Institut für Physik,
Johannes-Gutenberg Universität Mainz, 55099 Mainz
The half-filled Hubbard model on a Bethe-lattice with infinite coordination
number describes a Mott-Hubbard insulator above a critical
interaction strength. We extend our previous study [1] by using the Dynamical
Density-Matrix Renormalization Group method (DDMRG) [2,3]
to solve the Dynamical Mean-Field equations. To this end, we analyze a
single-impurity Anderson model with up to ns = 64 levels in the bath.
We refine our results in [1] which were limited to ns = 14 in exact diagonalization.
Furthermore, we extend our analytical results on the groundstate
energy of the Mott-Hubbard insulator, to ninth-order in the inverse
coupling strength.
[1] M.P. Eastwood, F. Gebhard, E. Kalinowski, S. Nishimoto, and R.M.
Noack, Eur. Phys. J. B 35, 155 (2003).
[2] E. Jeckelmann, Phys. Rev. B 66, 045114 (2002).
[3] F. Gebhard, E. Jeckelmann, S. Mahlert, S. Nishimoto, and R.M.
Noack, cond-mat/0306438.
TT 24.19 Mi 14:30 Poster A
Quartic Oscillator: Diagonalization by Continuous Unitary
Transformations — •Sébastien Dusuel und Götz S. Uhrig —
Zülpicherstr. 77, D-50937 Köln, Germany
The method of Continuous Unitary Transformations (CUTs) has been
applied successfully to various many-body Hamiltonians. We here consider
a simple model, namely a single quartic oscillator. Our aim is two-fold:
First, it can be used as a pedagogical and illustrative introduction to the
CUTs. Second, thanks to its simplicity, the quartic oscillator allows to
gain an intuition about the CUTs. Various generators of the transformations
are tested and their efficiency is compared. Various high-order
truncation schemes are equally analyzed. The results are also compared
to results from the functional renormalization group.