Critical behavior of weakly interacting bosons: A functional renormalization group approach
| dc.creator | Hasselmann, Nils | |
| dc.creator | Ledowski, Sascha | |
| dc.creator | Kopietz, Peter | |
| dc.date | 2004-09-07 | |
| dc.date.accessioned | 2026-07-07T07:53:59Z | |
| dc.date.available | 2026-07-07T07:53:59Z | |
| dc.description | 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 and the short-wavelength 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. | |
| dc.description | 23 pages, 7 figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0409167 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0409167 | |
| dc.identifier | Physical Review A 70, 063621 (2004) | |
| dc.identifier | doi:10.1103/PhysRevA.70.063621 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126435 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Critical behavior of weakly interacting bosons: A functional renormalization group approach | |
| dc.type | text |