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arXiv:2607.18396

Quantum critical fan and emergent relativistic symmetry of two-dimensional Dirac semimetals

Friederike Ihssen, Bilal Hawashin, Mireia Tolosa-Simeón, Michael M. Scherer

Published Jul 20, 2026• 0 citations
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Abstract

Two-dimensional Dirac semimetals near a quantum critical point can be described by Gross--Neveu--Yukawa models. In view of recent experimental advances exhibiting a transition from Dirac semimetal to insulator in highly-tunable van-der-Waals heterostructures, a better understanding of finite-temperature effects is mandatory. Here, we study the Gross--Neveu--Yukawa phase diagram of the chiral Ising model with a non-perturbative field-theory approach at zero and finite temperature, both in the semimetallic phase and in the insulating phase with spontaneously broken $\mathbb{Z}_2$ symmetry. At zero temperature, we find a quantum critical point with critical exponents that are close to the ones of the chiral Ising universality class, and show that relativistic symmetry is emergent close to the quantum critical point. At finite temperature, the ordered phase survives up to a finite critical temperature, at which we observe a classical phase transition into the disordered phase. We confirm that this transition lies in the two-dimensional Ising universality class. Finally, we determine the extent and scaling properties of the quantum critical fan, and the behavior of the quasiparticle weight, therein. In summary, we present a unified field-theoretical framework for the phase diagram of the chiral Ising model in the surroundings of its quantum critical point.

DOI
10.48550/arxiv.2607.18396

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