Abstract
Lorentz symmetry appears as a quite robust feature of the strongly interacting Dirac materials even though the lattice interactions break such a symmetry. We here demonstrate that the Lorentz symmetry is restored at the quantum-critical point (QCP) separating the tilted Dirac semimetal, breaking this symmetry already at the noninteracting level, from a gapped s-wave superconducting instability. To this end, we employ a one-loop ϵ = (3 − D)-expansion close to the D = 3 upper critical dimension of the corresponding Gross-Neveu-Yukawa field theory. In particular, we show that the tilt parameter is irrelevant and ultimately vanishes at the QCP separating the two phases. In fact, as we argue here, such a Lorentz symmetry restoration may be generic for the strongly interacting tilted Dirac semimetals, irrespective of whether they feature mirror-symmetric or mirror-asymmetric tilting, and is also insensitive to whether the instability represents an insulator or a gapped superconductor. The proposed scenario can be tested in the quantum Monte Carlo simulations of the interacting tilted Dirac fermion lattice models.
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Acknowledgments
We thank Bitan Roy for fruitful discussions. This work was supported by the Swedish Research Council Grant No. VR 2019-04735 (V.J.), Fondecyt (Chile) Grant No. 1230933 (V.J.) and ANID/ACT210100 (V.J.).
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Reiser, P., Juričić, V. Tilted Dirac superconductor at quantum criticality: restoration of Lorentz symmetry. J. High Energ. Phys. 2024, 181 (2024). https://doi.org/10.1007/JHEP02(2024)181
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DOI: https://doi.org/10.1007/JHEP02(2024)181