130 research outputs found
The Dynamical Mean Field Theory phase space extension and critical properties of the finite temperature Mott transition
We consider the finite temperature metal-insulator transition in the half
filled paramagnetic Hubbard model on the infinite dimensional Bethe lattice. A
new method for calculating the Dynamical Mean Field Theory fixpoint surface in
the phase diagram is presented and shown to be free from the convergence
problems of standard forward recursion. The fixpoint equation is then analyzed
using dynamical systems methods. On the fixpoint surface the eigenspectra of
its Jacobian is used to characterize the hysteresis boundaries of the first
order transition line and its second order critical end point. The critical
point is shown to be a cusp catastrophe in the parameter space, opening a
pitchfork bifurcation along the first order transition line, while the
hysteresis boundaries are shown to be saddle-node bifurcations of two merging
fixpoints. Using Landau theory the properties of the critical end point is
determined and related to the critical eigenmode of the Jacobian. Our findings
provide new insights into basic properties of this intensively studied
transition.Comment: 11 pages, 12 figures, 1 tabl
The Dynamical Mean Field Theory phase space extension and critical properties of the finite temperature Mott transition
We consider the finite temperature metal-insulator transition in the half
filled paramagnetic Hubbard model on the infinite dimensional Bethe lattice. A
new method for calculating the Dynamical Mean Field Theory fixpoint surface in
the phase diagram is presented and shown to be free from the convergence
problems of standard forward recursion. The fixpoint equation is then analyzed
using dynamical systems methods. On the fixpoint surface the eigenspectra of
its Jacobian is used to characterize the hysteresis boundaries of the first
order transition line and its second order critical end point. The critical
point is shown to be a cusp catastrophe in the parameter space, opening a
pitchfork bifurcation along the first order transition line, while the
hysteresis boundaries are shown to be saddle-node bifurcations of two merging
fixpoints. Using Landau theory the properties of the critical end point is
determined and related to the critical eigenmode of the Jacobian. Our findings
provide new insights into basic properties of this intensively studied
transition.Comment: 11 pages, 12 figures, 1 tabl
Clustering in mixing flows
We calculate the Lyapunov exponents for particles suspended in a random
three-dimensional flow, concentrating on the limit where the viscous damping
rate is small compared to the inverse correlation time. In this limit Lyapunov
exponents are obtained as a power series in epsilon, a dimensionless measure of
the particle inertia. Although the perturbation generates an asymptotic series,
we obtain accurate results from a Pade-Borel summation. Our results prove that
particles suspended in an incompressible random mixing flow can show pronounced
clustering when the Stokes number is large and we characterise two distinct
clustering effects which occur in that limit.Comment: 5 pages, 1 figur
Unmixing in Random Flows
We consider particles suspended in a randomly stirred or turbulent fluid.
When effects of the inertia of the particles are significant, an initially
uniform scatter of particles can cluster together. We analyse this 'unmixing'
effect by calculating the Lyapunov exponents for dense particles suspended in
such a random three-dimensional flow, concentrating on the limit where the
viscous damping rate is small compared to the inverse correlation time of the
random flow (that is, the regime of large Stokes number). In this limit
Lyapunov exponents are obtained as a power series in a parameter which is a
dimensionless measure of the inertia. We report results for the first seven
orders. The perturbation series is divergent, but we obtain accurate results
from a Pade-Borel summation. We deduce that particles can cluster onto a
fractal set and show that its dimension is in satisfactory agreement with
previously reported in simulations of turbulent Navier-Stokes flows. We also
investigate the rate of formation of caustics in the particle flow.Comment: 39 pages, 8 figure
A class of ansatz wave functions for 1D spin systems and their relation to DMRG
We investigate the density matrix renormalization group (DMRG) discovered by
White and show that in the case where the renormalization eventually converges
to a fixed point the DMRG ground state can be simply written as a ``matrix
product'' form. This ground state can also be rederived through a simple
variational ansatz making no reference to the DMRG construction. We also show
how to construct the ``matrix product'' states and how to calculate their
properties, including the excitation spectrum. This paper provides details of
many results announced in an earlier letter.Comment: RevTeX, 49 pages including 4 figures (macro included). Uuencoded with
uufiles. A complete postscript file is available at
http://fy.chalmers.se/~tfksr/prb.dmrg.p
Staggered flux and stripes in doped antiferromagnets
We have numerically investigated whether or not a mean-field theory of spin
textures generate fictitious flux in the doped two dimensional -model.
First we consider the properties of uniform systems and then we extend the
investigation to include models of striped phases where a fictitious flux is
generated in the domain wall providing a possible source for lowering the
kinetic energy of the holes. We have compared the energetics of uniform systems
with stripes directed along the (10)- and (11)-directions of the lattice,
finding that phase-separation generically turns out to be energetically
favorable. In addition to the numerical calculations, we present topological
arguments relating flux and staggered flux to geometric properties of the spin
texture. The calculation is based on a projection of the electron operators of
the model into a spin texture with spinless fermions.Comment: RevTex, 19 pages including 20 figure
Application of Uniform Matrix Product State to Quantum Phase Transition with a Periodicity Change
As a method beyond the mean-field analysis, a matrix product state (MPS) with
incommensurate periodicity is applied to detect phase transitions accompanied
with periodicity change, where the incommensurate MPS is generated by acting
local-spin-rotation operators with the incommensurate periodicity on a uniform
MPS. As a commensurate/commensurate change, we calculate the partial ferro --
perfect ferro phase transition in the Heisenberg model and its critical
exponent of the magnetization curve. As a commensurate/incommensurate change,
we calculate the S=1 Heisenberg model with bilinear and biquadratic
interactions which has periodicity change in the spin-spin correlation
function.Comment: 4 pages, 3 figures, Supplement (Proc. TOKIMEKI2011) Program
No.25-P-3
Product Wave Function Renormalization Group: construction from the matrix product point of view
We present a construction of a matrix product state (MPS) that approximates
the largest-eigenvalue eigenvector of a transfer matrix T, for the purpose of
rapidly performing the infinite system density matrix renormalization group
(DMRG) method applied to two-dimensional classical lattice models. We use the
fact that the largest-eigenvalue eigenvector of T can be approximated by a
state vector created from the upper or lower half of a finite size cluster.
Decomposition of the obtained state vector into the MPS gives a way of
extending the MPS, at the system size increment process in the infinite system
DMRG algorithm. As a result, we successfully give the physical interpretation
of the product wave function renormalization group (PWFRG) method, and obtain
its appropriate initial condition.Comment: 8 pages, 8 figure
No evidence for UV-based nest-site selection in sticklebacks
BACKGROUND: Nests are built in various animal taxa including fish. In systems with exclusive male parental care, the choice of a nest site may be an important component of male fitness. The nest site may influence male attractiveness as a mate, and male, embryo, and juvenile survival probabilities. Reproductively active three-spined stickleback males establish and defend a territory in which they build a nest. Territories can differ remarkably in qualities that influence male and female reproductive success like predation risk or abiotic factors such as dissolved oxygen concentration or lighting conditions. The latter may be important because in sticklebacks the extended visual capability into the ultraviolet (UV) wave range plays a role in female mate choice. Males are thus expected to be choosy about the habitat in which they will build their nest. RESULTS: We tested nest-site choice in male three-spined sticklebacks with respect to different UV lighting conditions. Reproductively active males were given the simultaneous choice to build their nest either in an UV-rich (UV+) or an UV-lacking (UV-) environment. Males exhibited no significant nest-site preferences with respect to UV+ or UV-. However, larger males and also heavier ones completed their nests earlier. CONCLUSION: We found that UV radiation as well as differences in luminance had no influence on nest-site choice in three-spined sticklebacks. Males that built in the UV-rich environment were not different in any trait (body traits and UV reflection traits) from males that built in the UV-poor environment. There was a significant effect of standard length and body mass on the time elapsed until nest completion in the UV experiment. The larger and heavier a male, the faster he completed his nest. In the brightness control experiment there was a significant effect only of body mass on the duration of nest completion. Whether nest building preferences with respect to UV lighting conditions are context dependent needs to be tested for instance by nest-site choice experiment under increased predation risk
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