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

• URL: http://arxiv.org/abs/2405.08198v1
• Date: Mon, 13 May 2024 21:27:23 GMT
• Title: Generalized Hertz action and quantum criticality of two-dimensional Fermi systems
• Authors: Mateusz Homenda, Paweł Jakubczyk, Hiroyuki Yamase,
• Abstract summary: We reassess the structure of the effective action and quantum critical singularities of two-dimensional Fermi systems. We derive a generalized form of the Hertz action, which does not suffer from problems of singular effective interactions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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