137 research outputs found
Renormalization of the BCS-BEC crossover by order parameter fluctuations
We use the functional renormalization group approach with partial
bosonization in the particle-particle channel to study the effect of order
parameter fluctuations on the BCS-BEC crossover of superfluid fermions in three
dimensions. Our approach is based on a new truncation of the vertex expansion
where the renormalization group flow of bosonic two-point functions is closed
by means of Dyson-Schwinger equations and the superfluid order parameter is
related to the single particle gap via a Ward identity. We explicitly calculate
the chemical potential, the single-particle gap, and the superfluid order
parameter at the unitary point and compare our results with experiments and
previous calculations.Comment: 5 pages, 3 figure
Thermalization of magnons in yttrium-iron garnet: nonequilibrium functional renormalization group approach
Using a nonequilibrium functional renormalization group (FRG) approach we
calculate the time evolution of the momentum distribution of a magnon gas in
contact with a thermal phonon bath. As a cutoff for the FRG procedure we use a
hybridization parameter {\Lambda} giving rise to an artificial damping of the
phonons. Within our truncation of the FRG flow equations the time evolution of
the magnon distribution is obtained from a rate equation involving
cutoff-dependent nonequilibrium self-energies, which in turn satisfy FRG flow
equations depending on cutoff-dependent transition rates. Our approach goes
beyond the Born collision approximation and takes the feedback of the magnons
on the phonons into account. We use our method to calculate the thermalization
of a quasi two-dimensional magnon gas in the magnetic insulator yttrium-iron
garnet after a highly excited initial state has been generated by an external
microwave field. We obtain good agreement with recent experiments.Comment: 16 pages, 6 figures, final versio
Dynamic structure factor of Luttinger liquids with quadratic energy dispersion and long-range interactions
We calculate the dynamic structure factor S (omega, q) of spinless fermions
in one dimension with quadratic energy dispersion k^2/2m and long range
density-density interaction whose Fourier transform f_q is dominated by small
momentum-transfers q << q_0 << k_F. Here q_0 is a momentum-transfer cutoff and
k_F is the Fermi momentum. Using functional bosonization and the known
properties of symmetrized closed fermion loops, we obtain an expansion of the
inverse irreducible polarization to second order in the small parameter q_0 /
k_F. In contrast to perturbation theory based on conventional bosonization, our
functional bosonization approach is not plagued by mass-shell singularities.
For interactions which can be expanded as f_q = f_0 + f_0^{2} q^2/2 + O (q^4)
with finite f_0^{2} we show that the momentum scale q_c = 1/ | m f_0^{2} |
separates two regimes characterized by a different q-dependence of the width
gamma_q of the collective zero sound mode and other features of S (omega, q).
For q_c << q << k_F we find that the line-shape in this regime is
non-Lorentzian with an overall width gamma_q of order q^3/(m q_c) and a
threshold singularity at the lower edge.Comment: 33 Revtex pages, 17 figure
Quantum criticality of dipolar spin chains
We show that a chain of Heisenberg spins interacting with long-range dipolar
forces in a magnetic field h perpendicular to the chain exhibits a quantum
critical point belonging to the two-dimensional Ising universality class.
Within linear spin-wave theory the magnon dispersion for small momenta k is
[Delta^2 + v_k^2 k^2]^{1/2}, where Delta^2 \propto |h - h_c| and v_k^2 \propto
|ln k|. For fields close to h_c linear spin-wave theory breaks down and we
investigate the system using density-matrix and functional renormalization
group methods. The Ginzburg regime where non-Gaussian fluctuations are
important is found to be rather narrow on the ordered side of the transition,
and very broad on the disordered side.Comment: 6 pages, 5 figure
Absence of fermionic quasi-particles in the superfluid state of the attractive Fermi gas
We calculate the effect of order parameter fluctuations on the fermionic
single-particle excitations in the superfluid state of neutral fermions
interacting with short range attractive forces. We show that in dimensions D
\leq 3 the singular effective interaction between the fermions mediated by the
gapless Bogoliubov-Anderson mode prohibits the existence of well-defined
quasi-particles. We explicitly calculate the single-particle spectral function
in the BEC regime in D=3 and show that in this case the quasi-particle residue
and the density of states are logarithmically suppressed.Comment: 4 RevTex pages, 3 figures; title changed, new Figure 1, added
references. We argue that in the entire regime of the BCS-BEC crossover the
quasi-particle picture breaks down in D <=3 for neutral fermions (but NOT for
charged fermions
Quasi-particle behavior of composite fermions in the half-filled Landau level
We calculate the effect of infrared fluctuations of the Chern-Simons gauge
field on the single-particle Green's function of composite fermions in the
half-filled Landau level via higher-dimensional bosonization on a curved Fermi
surface. We find that composite fermions remain well-defined quasi-particles,
with an effective mass given by the mean-field value, but with anomalously
large damping and a spectral function that contains considerable weight away
from the quasi-particle peak.Comment: reference added; accepted for publication in Phys. Rev. Let
Density-density propagator for one-dimensional interacting spinless fermions with non-linear dispersion and calculation of the Coulomb drag resistivity
Using bosonization-fermionization transformation we map the
Tomonaga-Luttinger model of spinless fermions with non-linear dispersion on the
model of fermionic quasiparticles whose interaction is irrelevant in the
renormalization group sense. Such mapping allows us to set up an expansion for
the density-density propagator of the original Tomonaga-Luttinger Hamiltonian
in orders of the (irrelevant) quasiparticle interaction. The lowest order term
in such an expansion is proportional to the propagator for free fermions. The
next term is also evaluated. The propagator found is used for calculation of
the Coulomb drug resistivity in a system of two capacitively coupled
one-dimensional conductors. It is shown that is proportional to for
both free and interacting fermions. The marginal repulsive in-chain interaction
acts to reduce as compared to the non-interacting result. The correction to
due to the quasiparticle interaction is found as well. It scales as
at low temperature.Comment: 5 pages, 1 eps figure; the new version of the e-print corrects an
error, which exists in the original submission; fortunately, all important
conclusions of the study remain vali
Spin conductance, dynamic spin stiffness and spin diffusion in itinerant magnets
We discuss analogies between the charge- and spin response functions of
itinerant magnets. We show that the spin-analog of the charge stiffness is not
given by the usual spin stiffness rho_s, but by the dynamic spin stiffness D_s,
which is obtained from the dynamic spin conductance G_s (omega) in the limit of
vanishing frequency omega. The low-frequency behavior of G_s (omega) is used to
define ideal spin conductors, normal spin conductors, and spin insulators.
Assuming diffusive spin dynamics, we show that the spin diffusion coefficient
is proportional to lim_{omega rightarrow 0} {Re} {G}_s (omega). We exploit this
fact to develop a new extrapolation scheme for the spin diffusion coefficient
in the paramagnetic phase of the Hubbard model.Comment: Discussion of gauge invariance and difference between transverse and
longitudinal response added. Accepted for publication in Phys. Rev.
Critical behavior of weakly interacting bosons: A functional renormalization group approach
We present a detailed investigation of the momentum-dependent self-energy
Sigma(k) at zero frequency of weakly interacting bosons at the critical
temperature T_c of Bose-Einstein condensation in dimensions 3<=D<4. Applying
the functional renormalization group, we calculate the universal scaling
function for the self-energy at zero frequency but at all wave vectors within
an approximation which truncates the flow equations of the irreducible vertices
at the four-point level. The self-energy interpolates between the critical
regime k > k_c, where k_c is the
crossover scale. In the critical regime, the self-energy correctly approaches
the asymptotic behavior Sigma(k) \propto k^{2 - eta}, and in the
short-wavelength regime the behavior is Sigma(k) \propto k^{2(D-3)} in D>3. In
D=3, we recover the logarithmic divergence Sigma(k) \propto ln(k/k_c)
encountered in perturbation theory. Our approach yields the crossover scale k_c
as well as a reasonable estimate for the critical exponent eta in D=3. From our
scaling function we find for the interaction-induced shift in T_c in three
dimensions, Delta T_c / T_c = 1.23 a n^{1/3}, where a is the s-wave scattering
length and n is the density, in excellent agreement with other approaches. We
also discuss the flow of marginal parameters in D=3 and extend our truncation
scheme of the renormalization group equations by including the six- and
eight-point vertex, which yields an improved estimate for the anomalous
dimension eta \approx 0.0513. We further calculate the constant lim_{k->0}
Sigma(k)/k^{2-eta} and find good agreement with recent Monte-Carlo data.Comment: 23 pages, 7 figure
Self-energy and critical temperature of weakly interacting bosons
Using the exact renormalization group we calculate the momentum-dependent
self-energy Sigma (k) at zero frequency of weakly interacting bosons at the
critical temperature T_c of Bose-Einstein condensation in dimensions 3 <= D <
4. We obtain the complete crossover function interpolating between the critical
regime k << k_c, where Sigma (k) propto k^{2 - eta}, and the short-wavelength
regime k >> k_c, where Sigma (k) propto k^{2 (D-3)} in D> 3 and Sigma (k)
\propto ln (k/k_c) in D=3. Our approach yields the crossover scale k_c on the
same footing with a reasonable estimate for the critical exponent eta in D=3.
From our Sigma (k) we find for the interaction-induced shift of T_c in three
dimensions Delta T_c / T_c approx 1.23 a n^{1/3}, where a is the s-wave
scattering length and n is the density.Comment: 4 pages,1 figur
- …