Abstract
We study quantum criticality of the magnetic field induced charge density wave (CDW) order in correlated spinless Dirac fermions on the $\pi$-flux square lattice at zero temperature as a prototypical example of the magnetic catalysis, by using the infinite density matrix renormalization group. It is found that the CDW order parameter $M(B)$ exhibits an anomalous magnetic field $(B)$ scaling behavior characteristic of the $(2+1)$-dimensional chiral Ising universality class near the quantum critical point, which leads to a strong enhancement of $M(B)$ compared with a mean field result. We also establish a global phase diagram in the interaction-magnetic field plane for the fermionic quantum criticality.
Highlights
Correlated Dirac semimetals are one of the most fundamental systems in condensed matter physics and in high-energy physics
Bosonic order parameter fluctuations are intimately coupled with gapless Dirac fermions, which results in nontrivial quantum critical behaviors depending on fermionic degrees of freedom in addition to the order parameter symmetry and dimensionality of the system [23]
We study quantum criticality of the fieldinduced charge density wave (CDW) order in spinless Dirac fermions on the two-dimensional π -flux square lattice, which is one of the simplest realizations of the magnetic catalysis
Summary
Correlated Dirac semimetals are one of the most fundamental systems in condensed matter physics and in high-energy physics. In the (2 + 1)-dimensional Gross-Neveu-Yukawa-type models, it is shown that in the limit of the large number of fermion flavors Nf corresponding to a mean-field approximation, the order parameter √behaves as M(B) ∼ B for weak interactions V Vc, M(B) ∼ B near the critical point V = Vc, and M(B) − M(0) ∼ B2 for strong interactions V Vc. the magnetic catalysis was first studied in high-energy physics, it was discussed in condensed matter physics, especially for graphene and related materials [36,37,38,39,40,41,42,43,44].
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