A Renormalization-Group Study of Interacting Bose-Einstein Condensates: II. Anomalous Dimension $\eta$ for $d\lesssim 4$ at Finite Temperatures

Abstract

We study the anomalous dimension $\eta$ of homogeneous interacting single-component Bose-Einstein condensates at finite temperatures for $d\lesssim 4$ dimensions. This $\eta$ is defined in terms of the one-particle density matrix $\rho (\mathbf{r})\equiv ⟨{\hat{\psi }}^{†}({\mathbf{r}}_1)\hat{\psi }({\mathbf{r}}_1+\mathbf{r})⟩$ through its asymptotic behavior $\rho (\mathbf{r})\to N_0/V+C{r}^{-d+2-\eta }$ for $r\to \infty$, where $N_0/V$ is the condensate density and $C$ is a constant. It is shown that the anomalous dimension is given by $\eta =0.181{\epsilon }^2$ to the leading order in $\epsilon \equiv d-4$. The change of the prefactor $0.181$ from the value $0.02$ at the transition point of the $\mathrm{O}(2)$ symmetric ${\varphi }^4$ model is attributed to the emergence of three-point vertices and the anomalous Green's function when $N_0$ acquires a finite value.

arXiv comment22 pages, 9 figures

References in corpus (8)

• Exact evolution equation for the effective potential
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• The Exact Renormalisation Group and Approximate Solutions
• Functional renormalization group approach to correlated fermion systems
• Functional renormalization group with vacuum expectation values and spontaneous symmetry breaking
• A Renormalization-Group Study of Interacting Bose-Einstein condensates: Absence of the Bogoliubov Mode below Four ($T>0$) and Three ($T=0$) Dimensions
• 3/2-Body Correlations and Coherence in Bose-Einstein Condensates
• Number-Phase Fluctuations in Isolated Superconductors

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