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arXiv · 2405.08198

Generalized Hertz action and quantum criticality of two-dimensional Fermi systems

Mateusz Homenda·Paweł Jakubczyk·Hiroyuki Yamase
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Abstract

We reassess the structure of the effective action and quantum critical singularities of two-dimensional Fermi systems characterized by the ordering wavevector $\vec{Q}= \vec{0}$. By employing infrared cutoffs on all the massless degrees of freedom, we derive a generalized form of the Hertz action, which does not suffer from problems of singular effective interactions. We demonstrate that the Wilsonian momentum-shell renormalization group (RG) theory capturing the infrared scaling should be formulated keeping $\vec{Q}$ as a flowing, scale-dependent quantity. At the quantum critical point, scaling controlled by the dynamical exponent $z=3$ is overshadowed by a broad scaling regime characterized by a lower value of $z \approx 2$. This in particular offers an explanation of the results of quantum Monte Carlo simulations pertinent to the electronic nematic quantum critical point.

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Mateusz Homenda, Paweł Jakubczyk, Hiroyuki Yamase. 2024-05-13. Generalized Hertz action and quantum criticality of two-dimensional Fermi systems. https://doi.org/10.1103/physrevb.110.l121102

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