Quantum criticality and spatial symmetry in interacting Dirac electrons under magnetic fields

Recently there have emerged various materials for strongly interacting Dirac electrons. Such systems are expected to provide an ideal platform for quantum phase transitions and quantum criticality. Interestingly, it is known that an ordered phase in a Dirac system gets stabilized under an external magnetic field, which is called magnetic catalysis in hadron physics. This implies that a magnetic field can control interaction effects in a Dirac system, especially quantum fluctuations associated with spontaneous symmetry breaking.

In this study, we discuss the quantum phase transition and criticality of an interacting Dirac electron system. After briefly introducing magnetic catalysis in our model [1], we examine orbital diamagnetism near the quantum critical point of a semimetal-insulator (charge density wave state) phase transition [2]. Especially, we show that the orbital magnetization exhibits a scaling behavior belonging to the (2+1)-dimensional chiral Ising universality class. We also discuss underlying spatial symmetry with a tiny magnetic field, which is spontaneously broken in ordered phases. It is found that the projective space group symmetry is not an exact but only approximate symmetry of the system under the small magnetic field [3]. Our results could provide a basic understanding of interacting Dirac electrons under magnetic fields.

[1] Y. Tada, “Quantum criticality in magnetic catalysis in two-dimensional correlated Dirac fermions”, Phys. Rev. Research 2, 033363 (2020).
[2] Y. Tada, “Quantum critical orbital diamagnetism in correlated Dirac system”, arXiv: 2106.04071.
[3] Y. Tada, “Lieb-Schultz-Mattis theorem in higher dimensions from approximate magnetic translation symmetry”, arXiv:2106.12222.