14 research outputs found
Spin susceptibility of interacting electrons in one dimension: Luttinger liquid and lattice effects
The temperature-dependent uniform magnetic susceptibility of interacting
electrons in one dimension is calculated using several methods. At low
temperature, the renormalization group reaveals that the Luttinger liquid spin
susceptibility approaches zero temperature with an infinite slope
in striking contrast with the Fermi liquid result and with the behavior of the
compressibility in the absence of umklapp scattering. This effect comes from
the leading marginally irrelevant operator, in analogy with the Heisenberg spin
1/2 antiferromagnetic chain. Comparisons with Monte Carlo simulations at higher
temperature reveal that non-logarithmic terms are important in that regime.
These contributions are evaluated from an effective interaction that includes
the same set of diagrams as those that give the leading logarithmic terms in
the renormalization group approach. Comments on the third law of thermodynamics
as well as reasons for the failure of approaches that work in higher dimensions
are given.Comment: 21 pages, latex including 5 eps figure
Effect of Inter-Site Repulsions on Magnetic Susceptibility of One-Dimensional Electron Systems at Quarter-Filling
The temperature dependence of the magnetic susceptibility, \chi (T), is
investigated for one-dimensional interacting electron systems at
quarter-filling within the Kadanoff-Wilson renormalization-group method.
The forward scattering on the same branch (the g_4-process) is examined
together with the backward (g_1) and forward (g_2) scattering amplitudes on
opposite branches.
In connection with lattice models, we show that \chi (T) is strongly enhanced
by the nearest-neighbor interaction, an enhancement that surpasses one of the
next-nearest-neighbor interaction.
A connection between our predictions for \chi (T) and experimental results
for \chi (T) in quasi-one-dimensional organic conductors is presented.Comment: 4 pages, 4 figures, to be published in Journal of the Physical
Society of Japan, vol. 74, No. 1
A finite element model to improve noise reduction based attenuation measurement of earmuffs in a directional sound field
The real attenuation of hearing protection devices (HPD) can be assessed in the field using a method based on continuous field microphone-in-real-ear (F-MIRE) measurements. The two-microphone method provides an indicator called the measured noise reduction (NRâ), defined as the difference between the measured exterior (outside the protector) and interior (under the protector) sound pressure levels (SPL). The HPD's attenuation expressed in terms of the more common insertion loss (IL) can then be obtained from NRâ using compensation factors. For earmuffs, NRâ has been shown to vary of up to 20 dB depending on the angle of incidence of the sound source. Therefore, there is a need to use sound incidence dependent compensation factors to relate NRâ and IL. To evaluate these factors and more generally to improve the continuous F-MIRE method, a finite-element (FE) model of an earmuff on an ATF (acoustic test fixture) exposed to a directional sound field has been developed and its predictions compared with lab measurements for several incidence angles. Regarding the external microphone SPL and the NRâ, in one-third of octave bands, the model correlates very well with measurements for frequencies below 1250 Hz whatever the sound incidence. Above 1250 Hz, the FE model captures the trends, as a function of the incidence angle, but the agreement generally decreases with increasing frequency. A better correlation between the FE model and the experimental data is achieved for the variation of NRâ (ÎNRâ) as a function of the sound incidence. Actions, such as (i) accounting for the headband in the model, (ii) refining the modeling of the sound source, (iii) improving the cushion modeling and (iv) better describing the backplate/cushion coupling conditions, are suggested to improve the model accuracy. To illustrate the potential of the modeling to improve the continuous F-MIRE measurement method, the FE model is used to determine an optimal position of the external microphone and to obtain estimates of exposure levels using the left and right ear exterior microphones. © 2016 Elsevier Lt
Effects of Next-Nearest-Neighbor Repulsion on One-Dimensional Quarter-Filled Electron Systems
We examine effects of the next-nearest-neighbor repulsion on electronic
states of a one-dimensional interacting electron system which consists of
quarter-filled band and interactions of on-site and nearest-neighbor repulsion.
We derive the effective Hamiltonian for the electrons around wave number \pm
\kf (\kf: Fermi wave number) and apply the renormalization group method to
the bosonized Hamiltonian. It is shown that the next-nearest-neighbor repulsion
makes 4\kf-charge ordering unstable and suppresses the spin fluctuation.
Further the excitation gaps and spin susceptibility are also evaluated.Comment: 19 pages, 8 figures, submitted to J. Phys. Soc. Jp
Role of Interchain Hopping in the Magnetic Susceptibility of Quasi-One-Dimensional Electron Systems
The role of interchain hopping in quasi-one-dimensional (Q-1D) electron
systems is investigated by extending the Kadanoff-Wilson renormalization group
of one-dimensional (1D) systems to Q-1D systems. This scheme is applied to the
extended Hubbard model to calculate the temperature () dependence of the
magnetic susceptibility, . The calculation is performed by taking
into account not only the logarithmic Cooper and Peierls channels, but also the
non-logarithmic Landau and finite momentum Cooper channels, which give relevant
contributions to the uniform response at finite temperatures. It is shown that
the interchain hopping, , reduces at low temperatures,
while it enhances at high temperatures. This notable
dependence is ascribed to the fact that enhances the
antiferromagnetic spin fluctuation at low temperatures, while it suppresses the
1D fluctuation at high temperatures. The result is at variance with the
random-phase-approximation approach, which predicts an enhancement of by over the whole temperature range. The influence of both the
long-range repulsion and the nesting deviations on is further
investigated. We discuss the present results in connection with the data of
in the (TMTTF) and (TMTSF) series of Q-1D organic
conductors, and propose a theoretical prediction for the effect of pressure on
magnetic susceptibility.Comment: 17 pages, 19figure
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
Two-Particle-Self-Consistent Approach for the Hubbard Model
Even at weak to intermediate coupling, the Hubbard model poses a formidable
challenge. In two dimensions in particular, standard methods such as the Random
Phase Approximation are no longer valid since they predict a finite temperature
antiferromagnetic phase transition prohibited by the Mermin-Wagner theorem. The
Two-Particle-Self-Consistent (TPSC) approach satisfies that theorem as well as
particle conservation, the Pauli principle, the local moment and local charge
sum rules. The self-energy formula does not assume a Migdal theorem. There is
consistency between one- and two-particle quantities. Internal accuracy checks
allow one to test the limits of validity of TPSC. Here I present a pedagogical
review of TPSC along with a short summary of existing results and two case
studies: a) the opening of a pseudogap in two dimensions when the correlation
length is larger than the thermal de Broglie wavelength, and b) the conditions
for the appearance of d-wave superconductivity in the two-dimensional Hubbard
model.Comment: Chapter in "Theoretical methods for Strongly Correlated Systems",
Edited by A. Avella and F. Mancini, Springer Verlag, (2011) 55 pages.
Misprint in Eq.(23) corrected (thanks D. Bergeron
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