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arXiv 1203.4432cond-mat.quant-gas
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玻色子-费米子混合体的单圈重整化群研究

One-loop renormalization group study of boson-fermion mixtures

Boyang Liu, Jiangping Hu

摘要:

利用Wisonian重整化群分析研究了弱相互作用玻色子-费米子混合模型。该模型包括一个玻色子-玻色子相互作用项和一个玻色子-费米子相互作用项。在树水平上计算了两个相互作用耦合常数的标度维数,在单圈水平上推导了Gell-Mann-Low方程。我们发现,在盖尔曼-洛方程的贡献费米子环走向零的长度尺度接近无穷大。在忽略费米子环贡献后,在三维情况下找到了两个不动点。一个是Gauss不动点,另一个是Wilson-Fisher不动点。我们发现玻色子-费米子相互作用在Wilson-Fisher不动点处是对称的。我们还观察到在RG变换下,玻色子-费米子相互作用耦合常数在一个小的负初值下趋于负无穷大,这表明玻色子-费米子配对不稳定性。进一步讨论了该模型中突现超对称性的可能性。

英文摘要:

A weakly interacting boson-fermion mixture model was investigated using Wisonian renormalization group analysis. This model includes one boson-boson interaction term and one boson-fermion interaction term. The scaling dimensions of the two interaction coupling constants were calculated as 2-D at tree level and the Gell-Mann-Low equations were derived at one-loop level. We find that in the Gell-Mann-Low equations the contributions from the fermion loops go to zero as the length scale approaches infinity. After ignoring the fermion loop contributions two fixed points were found in 3 dimensional case. One is the Gaussian fixed point and the other one is Wilson-Fisher fixed point. We find that the boson-fermion interaction decouples at the Wilson-Fisher fixed point. We also observe that under RG transformation the boson-fermion interaction coupling constant runs to negative infinity with a small negative initial value, which indicates a boson-fermion pairing instability. Furthermore, the possibility of emergent supersymmetry in this model was discussed.

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