7 research outputs found
Hole Dispersions for Antiferromagnetic Spin-1/2 Two-Leg Ladders by Self-Similar Continuous Unitary Transformations
The hole-doped antiferromagnetic spin-1/2 two-leg ladder is an important
model system for the high- superconductors based on cuprates. Using the
technique of self-similar continuous unitary transformations we derive
effective Hamiltonians for the charge motion in these ladders. The key
advantage of this technique is that it provides effective models explicitly in
the thermodynamic limit. A real space restriction of the generator of the
transformation allows us to explore the experimentally relevant parameter
space. From the effective Hamiltonians we calculate the dispersions for single
holes. Further calculations will enable the calculation of the interaction of
two holes so that a handle of Cooper pair formation is within reach.Comment: 16 pages, 26 figure
Adapted continuous unitary transformation to treat systems with quasiparticles of finite lifetime
An improved generator for continuous unitary transformations is introduced to
describe systems with unstable quasiparticles. Its general properties are
derived and discussed. To illustrate this approach we investigate the
asymmetric antiferromagnetic spin-1/2 Heisenberg ladder which allows for
spontaneous triplon decay. We present results for the low energy spectrum and
the momentum resolved spectral density of this system. In particular, we show
the resonance behavior of the decaying triplon explicitly.Comment: 40 pages, 12 figure
From Gapped Excitons to Gapless Triplons in One Dimension
Often, exotic phases appear in the phase diagrams between conventional
phases. Their elementary excitations are of particular interest. Here, we
consider the example of the ionic Hubbard model in one dimension. This model is
a band insulator (BI) for weak interaction and a Mott insulator (MI) for strong
interaction. Inbetween, a spontaneously dimerized insulator (SDI) occurs which
is governed by energetically low-lying charge and spin degrees of freedom.
Applying a systematically controlled version of the continuous unitary
transformations (CUTs) we are able to determine the dispersions of the
elementary charge and spin excitations and of their most relevant bound states
on equal footing. The key idea is to start from an externally dimerized system
using the relative weak interdimer coupling as small expansion parameter which
finally is set to unity to recover the original model.Comment: 18 pages, 10 figure
Functional renormalization group approach to zero-dimensional interacting systems
We apply the functional renormalization group method to the calculation of
dynamical properties of zero-dimensional interacting quantum systems. As case
studies we discuss the anharmonic oscillator and the single impurity Anderson
model. We truncate the hierarchy of flow equations such that the results are at
least correct up to second order perturbation theory in the coupling. For the
anharmonic oscillator energies and spectra obtained within two different
functional renormalization group schemes are compared to numerically exact
results, perturbation theory, and the mean field approximation. Even at large
coupling the results obtained using the functional renormalization group agree
quite well with the numerical exact solution. The better of the two schemes is
used to calculate spectra of the single impurity Anderson model, which then are
compared to the results of perturbation theory and the numerical
renormalization group. For small to intermediate couplings the functional
renormalization group gives results which are close to the ones obtained using
the very accurate numerical renormalization group method. In particulare the
low-energy scale (Kondo temperature) extracted from the functional
renormalization group results shows the expected behavior.Comment: 22 pages, 8 figures include
Strong-coupling expansion and effective hamiltonians
When looking for analytical approaches to treat frustrated quantum magnets,
it is often very useful to start from a limit where the ground state is highly
degenerate. This chapter discusses several ways of deriving {effective
Hamiltonians} around such limits, starting from standard {degenerate
perturbation theory} and proceeding to modern approaches more appropriate for
the derivation of high-order effective Hamiltonians, such as the perturbative
continuous unitary transformations or contractor renormalization. In the course
of this exposition, a number of examples taken from the recent literature are
discussed, including frustrated ladders and other dimer-based Heisenberg models
in a field, as well as the mapping between frustrated Ising models in a
transverse field and quantum dimer models.Comment: To appear as a chapter in "Highly Frustrated Magnetism", Eds. C.
Lacroix, P. Mendels, F. Mil
Truncation errors in self-similar continuous unitary transformations
Effects of truncation in self-similar continuous unitary transformations (S-CUT) are estimated rigorously. We find a formal description via an inhomogeneous flow equation. In this way, we are able to quantify truncation errors within the framework of the S-CUT and obtain rigorous error bounds for the ground state energy and the highest excited level. These bounds can be lowered exploiting symmetries of the Hamiltonian. We illustrate our approach with results for a toy model of two interacting hard-core bosons and the dimerized S=1/2 Heisenberg chain. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011