Critical behavior of weakly interacting bosons: A functional renormalizationgroup approach
Abstract
We present a detailed investigation of the momentumdependent selfenergy {sigma}(k) at zero frequency of weakly interacting bosons at the critical temperature T{sub c} of BoseEinstein condensation in dimensions 3{<=}D<4. Applying the functional renormalization group, we calculate the universal scaling function for the selfenergy at zero frequency but at all wave vectors within an approximation which truncates the flow equations of the irreducible vertices at the fourpoint level. The selfenergy interpolates between the critical regime k<<k{sub c} and the shortwavelength regime k>>k{sub c}, where k{sub c} is the crossover scale. In the critical regime, the selfenergy correctly approaches the asymptotic behavior {sigma}(k){proportional_to}k{sup 2{eta}}, and in the shortwavelength regime the behavior is {sigma}(k){proportional_to}k{sup 2(D3)} in D>3. In D=3, we recover the logarithmic divergence {sigma}(k){proportional_to}ln(k/k{sub c}) encountered in perturbation theory. Our approach yields the crossover scale k{sub c} as well as a reasonable estimate for the critical exponent {eta} in D=3. From our scaling function we find for the interactioninduced shift in T{sub c} in three dimensions, {delta}T{sub c}/T{sub c}=1.23an{sup 1/3}, where a is the swave 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 truncationmore »
 Authors:

 Institut fuer Theoretische Physik, Universitaet Frankfurt, RobertMayerStrasse 8, 60054 Frankfurt (Germany)
 Publication Date:
 OSTI Identifier:
 20649991
 Resource Type:
 Journal Article
 Journal Name:
 Physical Review. A
 Additional Journal Information:
 Journal Volume: 70; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevA.70.063621; (c) 2004 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 10502947
 Country of Publication:
 United States
 Language:
 English
 Subject:
 74 ATOMIC AND MOLECULAR PHYSICS; ANOMALOUS DIMENSION; BOSEEINSTEIN CONDENSATION; BOSONS; CRITICAL TEMPERATURE; DENSITY; INTERPOLATION; MONTE CARLO METHOD; PERTURBATION THEORY; RENORMALIZATION; S WAVES; SCATTERING LENGTHS; SELFENERGY; WAVELENGTHS
Citation Formats
Hasselmann, Nils, Ledowski, Sascha, and Kopietz, Peter. Critical behavior of weakly interacting bosons: A functional renormalizationgroup approach. United States: N. p., 2004.
Web. doi:10.1103/PhysRevA.70.063621.
Hasselmann, Nils, Ledowski, Sascha, & Kopietz, Peter. Critical behavior of weakly interacting bosons: A functional renormalizationgroup approach. United States. doi:10.1103/PhysRevA.70.063621.
Hasselmann, Nils, Ledowski, Sascha, and Kopietz, Peter. Wed .
"Critical behavior of weakly interacting bosons: A functional renormalizationgroup approach". United States. doi:10.1103/PhysRevA.70.063621.
@article{osti_20649991,
title = {Critical behavior of weakly interacting bosons: A functional renormalizationgroup approach},
author = {Hasselmann, Nils and Ledowski, Sascha and Kopietz, Peter},
abstractNote = {We present a detailed investigation of the momentumdependent selfenergy {sigma}(k) at zero frequency of weakly interacting bosons at the critical temperature T{sub c} of BoseEinstein condensation in dimensions 3{<=}D<4. Applying the functional renormalization group, we calculate the universal scaling function for the selfenergy at zero frequency but at all wave vectors within an approximation which truncates the flow equations of the irreducible vertices at the fourpoint level. The selfenergy interpolates between the critical regime k<<k{sub c} and the shortwavelength regime k>>k{sub c}, where k{sub c} is the crossover scale. In the critical regime, the selfenergy correctly approaches the asymptotic behavior {sigma}(k){proportional_to}k{sup 2{eta}}, and in the shortwavelength regime the behavior is {sigma}(k){proportional_to}k{sup 2(D3)} in D>3. In D=3, we recover the logarithmic divergence {sigma}(k){proportional_to}ln(k/k{sub c}) encountered in perturbation theory. Our approach yields the crossover scale k{sub c} as well as a reasonable estimate for the critical exponent {eta} in D=3. From our scaling function we find for the interactioninduced shift in T{sub c} in three dimensions, {delta}T{sub c}/T{sub c}=1.23an{sup 1/3}, where a is the swave 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 eightpoint vertex, which yields an improved estimate for the anomalous dimension {eta}{approx_equal}0.0513. We further calculate the constant lim{sub k0} {sigma}(k)/k{sup 2{eta}} and find good agreement with recent Monte Carlo data.},
doi = {10.1103/PhysRevA.70.063621},
journal = {Physical Review. A},
issn = {10502947},
number = 6,
volume = 70,
place = {United States},
year = {2004},
month = {12}
}