31 research outputs found
Phase Transition in Lattice Surface Systems with Gonihedric Action
We prove the existence of an ordered low temperature phase in a model of
soft-self-avoiding closed random surfaces on a cubic lattice by a suitable
extension of Peierls contour method. The statistical weight of each surface
configuration depends only on the mean extrinsic curvature and on an
interaction term arising when two surfaces touch each other along some contour.
The model was introduced by F.J. Wegner and G.K. Savvidy as a lattice version
of the gonihedric string, which is an action for triangulated random surfaces.Comment: 17 pages, Postscript figures include
Low temperature expansion of the gonihedric Ising model
We investigate a model of closed -dimensional soft-self-avoiding
random surfaces on a -dimensional cubic lattice. The energy of a surface
configuration is given by , where is the number of
edges, where two plaquettes meet at a right angle and is the number of
edges, where 4 plaquettes meet. This model can be represented as a
-spin system with ferromagnetic nearest-neighbour-, antiferromagnetic
next-nearest-neighbour- and plaquette-interaction. It corresponds to a special
case of a general class of spin systems introduced by Wegner and Savvidy. Since
there is no term proportional to the surface area, the bare surface tension of
the model vanishes, in contrast to the ordinary Ising model. By a suitable
adaption of Peierls argument, we prove the existence of infinitely many ordered
low temperature phases for the case . A low temperature expansion of the
free energy in 3 dimensions up to order () shows,
that for only the ferromagnetic low temperature phases remain stable. An
analysis of low temperature expansions up to order for the
magnetization, susceptibility and specific heat in 3 dimensions yields critical
exponents, which are in agreement with previous results.Comment: 27 pages, Postscript figures include
The Numerical Renormalization Group Method for correlated electrons
The Numerical Renormalization Group method (NRG) has been developed by Wilson
in the 1970's to investigate the Kondo problem. The NRG allows the
non-perturbative calculation of static and dynamic properties for a variety of
impurity models. In addition, this method has been recently generalized to
lattice models within the Dynamical Mean Field Theory. This paper gives a brief
historical overview of the development of the NRG and discusses its application
to the Hubbard model; in particular the results for the Mott metal-insulator
transition at low temperatures.Comment: 14 pages, 7 eps-figures include
Reentrant charge ordering caused by polaron formation
Based on a two-dimensional extended Hubbard model with electron-phonon
interaction, we have studied the effect of polaron formation on the charge
ordering (CO) transition. It is found that for fully ferromagnetically ordered
spins the CO state may go through a process of appearance, collapse and
reappearance with decreasing temperature. This is entirely due to a
emperature-dependent polaron bandwidth. On the other hand, when a paramagnetic
spin state is considered, only a simple reentrant behavior of the CO transition
is found, which is only partly due to polaron effect. This model is proposed as
an explanation of the observed reentrant behavior of the CO transition in the
layered manganite LaSrMnO.Comment: 4 pages, 2 eps figures, revised version accepted by Phys. Rev. Let
Finite temperature numerical renormalization group study of the Mott-transition
Wilson's numerical renormalization group (NRG) method for the calculation of
dynamic properties of impurity models is generalized to investigate the
effective impurity model of the dynamical mean field theory at finite
temperatures. We calculate the spectral function and self-energy for the
Hubbard model on a Bethe lattice with infinite coordination number directly on
the real frequency axis and investigate the phase diagram for the Mott-Hubbard
metal-insulator transition. While for T<T_c approx 0.02W (W: bandwidth) we find
hysteresis with first-order transitions both at U_c1 (defining the insulator to
metal transition) and at U_c2 (defining the metal to insulator transition), at
T>T_c there is a smooth crossover from metallic-like to insulating-like
solutions.Comment: 10 pages, 9 eps-figure
Phase diagram of the quarter-filled extended Hubbard model on a two-leg ladder
We investigate the ground-state phase diagram of the quarter-filled Hubbard
ladder with nearest-neighbor Coulomb repulsion V using the Density Matrix
Renormalization Group technique. The ground-state is homogeneous at small V, a
``checkerboard'' charge--ordered insulator at large V and not too small on-site
Coulomb repulsion U, and is phase-separated for moderate or large V and small
U. The zero-temperature transition between the homogeneous and the
charge-ordered phase is found to be second order. In both the homogeneous and
the charge-ordered phases the existence of a spin gap mainly depends on the
ratio of interchain to intrachain hopping. In the second part of the paper, we
construct an effective Hamiltonian for the spin degrees of freedom in the
strong-coupling charge-ordered regime which maps the system onto a frustrated
spin chain. The opening of a spin gap is thus connected with spontaneous
dimerization.Comment: 12 pages, 13 figures, submitted to PRB, presentation revised, new
results added (metallic phase at small U and V
Finite-Temperature Properties across the Charge Ordering Transition -- Combined Bosonization, Renormalization Group, and Numerical Methods
We theoretically describe the charge ordering (CO) metal-insulator transition
based on a quasi-one-dimensional extended Hubbard model, and investigate the
finite temperature () properties across the transition temperature, . In order to calculate dependence of physical quantities such as the
spin susceptibility and the electrical resistivity, both above and below
, a theoretical scheme is developed which combines analytical
methods with numerical calculations. We take advantage of the renormalization
group equations derived from the effective bosonized Hamiltonian, where Lanczos
exact diagonalization data are chosen as initial parameters, while the CO order
parameter at finite- is determined by quantum Monte Carlo simulations. The
results show that the spin susceptibility does not show a steep singularity at
, and it slightly increases compared to the case without CO because
of the suppression of the spin velocity. In contrast, the resistivity exhibits
a sudden increase at , below which a characteristic dependence
is observed. We also compare our results with experiments on molecular
conductors as well as transition metal oxides showing CO.Comment: 9 pages, 8 figure
Charge ordering and antiferromagnetic exchange in layered molecular crystals of the theta type
We consider the electronic properties of layered molecular crystals of the
type theta-DA, where A is an anion and D is a donor molecule such as
BEDT-TTF [where BEDT-TTF is bis-(ethylenedithia-tetrathiafulvalene)] which is
arranged in the theta type pattern within the layers. We argue that the
simplest strongly correlated electron model that can describe the rich phase
diagram of these materials is the extended Hubbard model on the square lattice
at a quarter filling. In the limit where the Coulomb repulsion on a single site
is large, the nearest-neighbour Coulomb repulsion, V, plays a crucial role.
When V is much larger than the intermolecular hopping integral t the ground
state is an insulator with charge ordering. In this phase antiferromagnetism
arises due to a novel fourth-order superexchange process around a plaquette on
the square lattice. We argue that the charge ordered phase is destroyed below a
critical non-zero value V, of the order of t. Slave boson theory is used to
explicitly demonstrate this for the SU(N) generalisation of the model, in the
large N limit. We also discuss the relevance of the model to the all-organic
family beta''-(BEDT-TTF)SFYSO where Y = CHCF, CH, CHF.Comment: 15 pages, 6 eps figure
The Hubbard model within the equations of motion approach
The Hubbard model has a special role in Condensed Matter Theory as it is
considered as the simplest Hamiltonian model one can write in order to describe
anomalous physical properties of some class of real materials. Unfortunately,
this model is not exactly solved except for some limits and therefore one
should resort to analytical methods, like the Equations of Motion Approach, or
to numerical techniques in order to attain a description of its relevant
features in the whole range of physical parameters (interaction, filling and
temperature). In this manuscript, the Composite Operator Method, which exploits
the above mentioned analytical technique, is presented and systematically
applied in order to get information about the behavior of all relevant
properties of the model (local, thermodynamic, single- and two- particle ones)
in comparison with many other analytical techniques, the above cited known
limits and numerical simulations. Within this approach, the Hubbard model is
shown to be also capable to describe some anomalous behaviors of the cuprate
superconductors.Comment: 232 pages, more than 300 figures, more than 500 reference