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Title: Critical behavior of weakly interacting bosons: A functional renormalization-group approach

Abstract

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{sub 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{sub c} and the short-wavelength regime k>>k{sub c}, where k{sub c} is the crossover scale. In the critical regime, the self-energy correctly approaches the asymptotic behavior {sigma}(k){proportional_to}k{sup 2-{eta}}, and in the short-wavelength regime the behavior is {sigma}(k){proportional_to}k{sup 2(D-3)} 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 interaction-induced shift in T{sub c} in three dimensions, {delta}T{sub c}/T{sub c}=1.23an{sup 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 truncationmore » 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_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.« less

Authors:
; ;  [1]
  1. Institut fuer Theoretische Physik, Universitaet Frankfurt, Robert-Mayer-Strasse 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 1050-2947
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; ANOMALOUS DIMENSION; BOSE-EINSTEIN CONDENSATION; BOSONS; CRITICAL TEMPERATURE; DENSITY; INTERPOLATION; MONTE CARLO METHOD; PERTURBATION THEORY; RENORMALIZATION; S WAVES; SCATTERING LENGTHS; SELF-ENERGY; WAVELENGTHS

Citation Formats

Hasselmann, Nils, Ledowski, Sascha, and Kopietz, Peter. Critical behavior of weakly interacting bosons: A functional renormalization-group 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 renormalization-group 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 renormalization-group approach". United States. doi:10.1103/PhysRevA.70.063621.
@article{osti_20649991,
title = {Critical behavior of weakly interacting bosons: A functional renormalization-group approach},
author = {Hasselmann, Nils and Ledowski, Sascha and Kopietz, Peter},
abstractNote = {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{sub 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{sub c} and the short-wavelength regime k>>k{sub c}, where k{sub c} is the crossover scale. In the critical regime, the self-energy correctly approaches the asymptotic behavior {sigma}(k){proportional_to}k{sup 2-{eta}}, and in the short-wavelength regime the behavior is {sigma}(k){proportional_to}k{sup 2(D-3)} 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 interaction-induced shift in T{sub c} in three dimensions, {delta}T{sub c}/T{sub c}=1.23an{sup 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_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 = {1050-2947},
number = 6,
volume = 70,
place = {United States},
year = {2004},
month = {12}
}