13,440 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
Low-temperature properties of the Hubbard model on highly frustrated one-dimensional lattices
We consider the repulsive Hubbard model on three highly frustrated
one-dimensional lattices -- sawtooth chain and two kagom\'{e} chains -- with
completely dispersionless (flat) lowest single-electron bands. We construct the
complete manifold of {\em exact many-electron} ground states at low electron
fillings and calculate the degeneracy of these states. As a result, we obtain
closed-form expressions for low-temperature thermodynamic quantities around a
particular value of the chemical potential . We discuss specific
features of thermodynamic quantities of these ground-state ensembles such as
residual entropy, an extra low-temperature peak in the specific heat, and the
existence of ferromagnetism and paramagnetism. We confirm our analytical
results by comparison with exact diagonalization data for finite systems.Comment: 20 pages, 12 figures, 2 table
The sawtooth chain: From Heisenberg spins to Hubbard electrons
We report on recent studies of the spin-half Heisenberg and the Hubbard model
on the sawtooth chain. For both models we construct a class of exact
eigenstates which are localized due to the frustrating geometry of the lattice
for a certain relation of the exchange (hopping) integrals. Although these
eigenstates differ in details for the two models because of the different
statistics, they share some characteristic features. The localized eigenstates
are highly degenerate and become ground states in high magnetic fields
(Heisenberg model) or at certain electron fillings (Hubbard model),
respectively. They may dominate the low-temperature thermodynamics and lead to
an extra low-temperature maximum in the specific heat. The ground-state
degeneracy can be calculated exactly by a mapping of the manifold of localized
ground states onto a classical hard-dimer problem, and explicit expressions for
thermodynamic quantities can be derived which are valid at low temperatures
near the saturation field for the Heisenberg model or around a certain value of
the chemical potential for the Hubbard model, respectively.Comment: 16 pages, 6 figure, the paper is based on an invited talk on the XXXI
International Workshop on Condensed Matter Theories, Bangkok, Dec 2007;
notation of x-axis in Fig.6 corrected, references update
Flat-Band Ferromagnetism as a Pauli-Correlated Percolation Problem
We investigate the location and nature of the para-ferro transition of
interacting electrons in dispersionless bands using the example of the Hubbard
model on the Tasaki lattice. This case can be analyzed as a geometric
site-percolation problem where different configurations appear with nontrivial
weights. We provide a complete exact solution for the 1D case and develop a
numerical algorithm for the 2D case. In two dimensions the paramagnetic phase
persists beyond the uncorrelated percolation point, and the grand-canonical
transition is via a first-order jump to an unsaturated ferromagnetic phase.Comment: 6 pages, 5 figure
Frustrated spin- Heisenberg magnet on a square-lattice bilayer: High-order study of the quantum critical behavior of the ---- model
The zero-temperature phase diagram of the spin-
---- model on an -stacked square-lattice
bilayer is studied using the coupled cluster method implemented to very high
orders. Both nearest-neighbor (NN) and frustrating next-nearest-neighbor
Heisenberg exchange interactions, of strengths and , respectively, are included in each layer. The two layers are
coupled via a NN interlayer Heisenberg exchange interaction with a strength
. The magnetic order parameter (viz.,
the sublattice magnetization) is calculated directly in the thermodynamic
(infinite-lattice) limit for the two cases when both layers have
antiferromagnetic ordering of either the N\'{e}el or the striped kind, and with
the layers coupled so that NN spins between them are either parallel (when
) to one another. Calculations
are performed at th order in a well-defined sequence of approximations,
which exactly preserve both the Goldstone linked cluster theorem and the
Hellmann-Feynman theorem, with . The sole approximation made is to
extrapolate such sequences of th-order results for to the exact limit,
. By thus locating the points where vanishes, we calculate
the full phase boundaries of the two collinear AFM phases in the
-- half-plane with . In particular, we provide the
accurate estimate, (), for the
position of the quantum triple point (QTP) in the region . We also
show that there is no counterpart of such a QTP in the region ,
where the two quasiclassical phase boundaries show instead an ``avoided
crossing'' behavior, such that the entire region that contains the nonclassical
paramagnetic phases is singly connected
Emergent Ising degrees of freedom in frustrated two-leg ladder and bilayer Heisenberg antiferromagnets
Based on exact diagonalization data for finite quantum Heisenberg
antiferromagnets on two frustrated lattices (two-leg ladder and bilayer) and
analytical arguments we map low-energy degrees of freedom of the spin models in
a magnetic field on classical lattice-gas models. Further we use
transfer-matrix calculations and classical Monte Carlo simulations to give a
quantitative description of low-temperature thermodynamics of the quantum spin
models. The classical lattice-gas model yields an excellent description of the
quantum spin models up to quite large temperatures. The main peculiarity of the
considered frustrated bilayer is a phase transition which occurs at low
temperatures for a wide range of magnetic fields below the saturation magnetic
field and belongs to the two-dimensional Ising model universality class.Comment: 17 pages, 8 figure
A solvable model of a random spin-1/2 XY chain
The paper presents exact calculations of thermodynamic quantities for the
spin-1/2 isotropic XY chain with random lorentzian intersite interaction and
transverse field that depends linearly on the surrounding intersite
interactions.Comment: 14 pages (Latex), 2 tables, 13 ps-figures included, (accepted for
publication in Phys.Rev.B
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