71 research outputs found
Recursion method and one-hole spectral function of the Majumdar-Ghosh model
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.Comment: 12 pages, 7 figure
Lieb-Mattis ferrimagnetism in diluted magnetic semiconductors
We show the possibility of long-range ferrimagnetic ordering with a
saturation magnetisation of the order of 1 Bohr magneton per spin for
arbitrarily low concentration of magnetic impurities in semiconductors,
provided that the impurities form a superstructure satisfying the conditions of
the Lieb-Mattis theorem. Explicit examples of such superstructures are given
for the wurtzite lattice, and the temperature of ferrimagnetic transition is
estimated from a high-temperature expansion. Exact diagonalization studies show
that small fragments of the structure exhibit enhanced magnetic response and
isotropic superparamagnetism at low temperatures. A quantum transition in a
high magnetic field is considered and similar superstructures in cubic
semiconductors are discussed as well.Comment: 6 pages,4 figure
Exact one- and two-particle excitation spectra of acute-angle helimagnets above their saturation magnetic field
The two-magnon problem for the frustrated XXZ spin-1/2 Heisenberg Hamiltonian
and external magnetic fields exceeding the saturation field Bs is considered.
We show that the problem can be exactly mapped onto an effective tight-binding
impurity problem. It allows to obtain explicit exact expressions for the
two-magnon Green's functions for arbitrary dimension and number of
interactions. We apply this theory to a quasi-one dimensional helimagnet with
ferromagnetic nearest neighbor J1 < 0 and antiferromagnetic next-nearest
neighbor J2 > 0 interactions. An outstanding feature of the excitation spectrum
is the existence of two-magnon bound states. This leads to deviations of the
saturation field Bs from its classical value Bs(classical) which coincides with
the one-magnon instability. For the refined frustration ratio |J2/J1|> 0.374661
the minimum of the two-magnon spectrum occurs at the boundary of the Brillouin
zone. Based on the two-magnon approach, we propose general analytic expressions
for the saturation field Bs, confirming known previous results for
one-dimensional isotropic systems, but explore also the role of interchain and
long-ranged intrachain interactions as well as of the exchange anisotropy.Comment: 21 pages, 6 Figures. submitted to Phys. Rev.
- …