6 research outputs found
Finding critical points using improved scaling Ansaetze
Analyzing in detail the first corrections to the scaling hypothesis, we
develop accelerated methods for the determination of critical points from
finite size data. The output of these procedures are sequences of
pseudo-critical points which rapidly converge towards the true critical points.
In fact more rapidly than previously existing methods like the Phenomenological
Renormalization Group approach. Our methods are valid in any spatial
dimensionality and both for quantum or classical statistical systems. Having at
disposal fast converging sequences, allows to draw conclusions on the basis of
shorter system sizes, and can be extremely important in particularly hard cases
like two-dimensional quantum systems with frustrations or when the sign problem
occurs. We test the effectiveness of our methods both analytically on the basis
of the one-dimensional XY model, and numerically at phase transitions occurring
in non integrable spin models. In particular, we show how a new Homogeneity
Condition Method is able to locate the onset of the
Berezinskii-Kosterlitz-Thouless transition making only use of ground-state
quantities on relatively small systems.Comment: 16 pages, 4 figures. New version including more general Ansaetze
basically applicable to all case
Unified picture of superfluidity: From Bogoliubov's approximation to Popov's hydrodynamic theory
Using a non-perturbative renormalization-group technique, we compute the
momentum and frequency dependence of the anomalous self-energy and the
one-particle spectral function of two-dimensional interacting bosons at zero
temperature. Below a characteristic momentum scale , where the Bogoliubov
approximation breaks down, the anomalous self-energy develops a square root
singularity and the Goldstone mode of the superfluid phase (Bogoliubov sound
mode) coexists with a continuum of excitations, in agreement with the
predictions of Popov's hydrodynamic theory. Thus our results provide a unified
picture of superfluidity in interacting boson systems and connect Bogoliubov's
theory (valid for momenta larger than ) to Popov's hydrodynamic approach.Comment: v2) 4 pages, 4 figures v3) Revised title + minor change
Infrared behavior and spectral function of a Bose superfluid at zero temperature
In a Bose superfluid, the coupling between transverse (phase) and
longitudinal fluctuations leads to a divergence of the longitudinal correlation
function, which is responsible for the occurrence of infrared divergences in
the perturbation theory and the breakdown of the Bogoliubov approximation. We
report a non-perturbative renormalization-group (NPRG) calculation of the
one-particle Green function of an interacting boson system at zero temperature.
We find two regimes separated by a characteristic momentum scale
("Ginzburg" scale). While the Bogoliubov approximation is valid at large
momenta and energies, |\p|,|\w|/c\gg k_G (with the velocity of the
Bogoliubov sound mode), in the infrared (hydrodynamic) regime |\p|,|\w|/c\ll
k_G the normal and anomalous self-energies exhibit singularities reflecting
the divergence of the longitudinal correlation function. In particular, we find
that the anomalous self-energy agrees with the Bogoliubov result
\Sigan(\p,\w)\simeq\const at high-energies and behaves as \Sigan(\p,\w)\sim
(c^2\p^2-\w^2)^{(d-3)/2} in the infrared regime (with the space
dimension), in agreement with the Nepomnyashchii identity \Sigan(0,0)=0 and
the predictions of Popov's hydrodynamic theory. We argue that the hydrodynamic
limit of the one-particle Green function is fully determined by the knowledge
of the exponent characterizing the divergence of the longitudinal
susceptibility and the Ward identities associated to gauge and Galilean
invariances. The infrared singularity of \Sigan(\p,\w) leads to a continuum
of excitations (coexisting with the sound mode) which shows up in the
one-particle spectral function.Comment: v1) 23 pages, 11 figures. v2) Changes following referee's comments.
To appear in Phys. Rev.A. v3) Typos correcte
Non-perturbative renormalization-group approach to zero-temperature Bose systems
We use a non-perturbative renormalization-group technique to study
interacting bosons at zero temperature. Our approach reveals the instability of
the Bogoliubov fixed point when and yields the exact infrared
behavior in all dimensions within a rather simple theoretical framework.
It also enables to compute the low-energy properties in terms of the parameters
of a microscopic model. In one-dimension and for not too strong interactions,
it yields a good picture of the Luttinger-liquid behavior of the superfluid
phase.Comment: v1) 6 pages, 8 figures; v2) added references; v3) corrected typo
Infrared behavior of interacting bosons at zero temperature
We review the infrared behavior of interacting bosons at zero temperature.
After a brief discussion of the Bogoliubov approximation and the breakdown of
perturbation theory due to infrared divergences, we present two approaches that
are free of infrared divergences -- Popov's hydrodynamic theory and the
non-perturbative renormalization group -- and allow us to obtain the exact
infrared behavior of the correlation functions. We also point out the
connection between the infrared behavior in the superfluid phase and the
critical behavior at the superfluid--Mott-insulator transition in the
Bose-Hubbard model.Comment: 8 pages, 4 figures. Proceedings of the 19th International Laser
Physics Workshop, LPHYS'10 (Foz do Iguacu, Brazil, July 5-9, 2010