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arXiv · 2410.22166

Mean-field theory for self-interacting relativistic Luttinger fermions

Holger Gies·Marta Picciau
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Abstract

We investigate a class of quantum field theories with relativistic Luttinger fermions and local self-interaction in scalar channels. For an understanding of possible low-energy phases, we first classify the set of mass terms arising from scalar fermion bilinears. For large flavor numbers, we show that each of our models features a coupling branch in which the theory is asymptotically free. In order to address the long-range behavior, we use mean-field theory which is exact in the limit of large flavor numbers. We identify two models which undergo dimensional transmutation, interconnecting the asymptotically free high-energy regime with an ordered low-energy phase sustaining a vacuum condensate. We also study the analytic structure of the Luttinger-fermionic propagator in the various possible gapped phases.

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Holger Gies, Marta Picciau. 2025-06-26. Mean-field theory for self-interacting relativistic Luttinger fermions. https://doi.org/10.1103/physrevd.111.085001

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