Anomalous scaling at the quantum critical point

Ar. Abanov; A. Chubukov

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Anomalous scaling at the quantum critical point

Ar. Abanov·A. Chubukov

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Abstract

We show that Hertz $ϕ^4$ theory of quantum criticality is incomplete as it misses anomalous non-local contributions to the interaction vertices. For antiferromagnetic quantum transitions, we found that the theory is renormalizable only if the dynamical exponent $z=2$. The upper critical dimension is still $d= 4-z =2$, however the number of marginal vertices at $d=2$ is infinite. As a result, the theory has a finite anomalous exponent already at the upper critical dimension. We show that for $d<2$ the Gaussian fixed point splits into two non-Gaussian fixed points. For both fixed points, the dynamical exponent remains $z=2$.

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Ar. Abanov, A. Chubukov. 2004-09-22. Anomalous scaling at the quantum critical point. https://arxiv.org/abs/cond-mat/0409601

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