https://doi.org/10.1140/epjb/e2003-00252-x
Recursion method and one-hole spectral function of the Majumdar-Ghosh model
1
Institute for Materials Science, Ukrainian Academy of
Sciences,
Krzhizhanovskogo 3, 03180 Kiev, Ukraine
2
Leibniz-Institut für Festkörper- und
Werkstoffforschung Dresden,
PO Box 270016, 01171 Dresden, Germany
3
Laboratoire Matériaux et Microélectronique de Provence,
49, rue Joliot-Curie, IRPHE, 13384 Marseille Cedex 13, France
4
Institut für Theoretische Physik,
Otto-von-Guericke Universität Magdeburg,
PO Box 4120, 39016 Magdeburg, Germany
Corresponding author: a R.Hayn@ifw-dresden.de
Received:
26
February
2003
Published online:
22
September
2003
We consider the application of the recursion method to the calculation of
one-particle Green's functions for strongly correlated systems and propose a
new way how to extract the information about the infinite system from the
exact diagonalisation of small clusters. Comparing the results for several
cluster sizes allows us to establish those Lanczos coefficients that are not
affected by the finite size effects and provide the information about the
Green's function of the macroscopic system. The analysis of this
`bulk-related' subset of coefficients supplemented by alternative analytic
approaches allows to infer their asymptotic behaviour and to propose an
approximate analytical form for the `terminator' of the Green's function
continued fraction expansion for the infinite system. As a result, the
Green's function acquires the branch cut singularity corresponding to the
incoherent part of the spectrum. The method is applied to the spectral
function of one-hole in the Majumdar-Ghosh model (the one-dimensional model at
). For this model, the branch
cut starts at finite energy
, but there is no upper bound of the
spectrum, corresponding to a linear increase of the recursion coefficients.
Further characteristics of the spectral function are band gaps in the middle
of the band and bound states below
or within the gaps. The band
gaps arise due to the period doubling of the unit cell and show up as
characteristic oscillations of the recursion coefficients on top of the
linear increase.
PACS: 75.10.Pq – Spin chain models / 71.10.Pm – Fermions in reduced dimensions / 71.27.+a – Strongly correlated electron systems; heavy fermions
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2003