Abstract We study orbital diamagnetism at zero temperature in (2 + 1)-dimensional Dirac fermions with a short-range interaction which exhibits a quantum phase transition to a charge density wave (CDW) phase. We introduce orbital magnetic fields into spinless Dirac fermions on the π-flux square lattice, and analyze them by using infinite density matrix renormalization group. It is found that the diamagnetism remains intact in the Dirac semimetal regime, while it is monotonically suppressed in the CDW regime. Around the quantum critical point of the CDW phase transition, we find a scaling behavior of the diamagnetism characteristic of the chiral Ising universality class. Besides, the scaling analysis implies that the robust orbital diamagnetism at weak magnetic fields in a Dirac semimetal regime would hold not only in our model but also in other interacting Dirac fermion systems as long as scaling regions are wide enough. The scaling behavior may also be regarded as a quantum, magnetic analogue of the critical Casimir effect which has been widely studied for classical phase transitions.
We present evidence that two dimensional Dirac fermions in the presence of random Abelian gauge potential exhibit a phase transition when the disorder strength exceeds a certain critical value. We argue that this phase transition has novel properties unique to disordered systems. It resembles in many ways the transition from dilute to dense polymers phase in two dimension. In particular, we argue that the central charge of the disordered Dirac fermions, being
c=0 before the transition, changes to
c=−2. We discuss possible implications to quantum Hall transitions, in view of recently proposed model for quantum Hall transitions with
c=−2.