Robust orbital diamagnetism of correlated Dirac fermions in chiral Ising universality class

Abstract

We study orbital diamagnetism in (2 + 1)-dimensional Dirac electrons with a short-range interaction at zero temperature. We introduce orbital magnetic fields into spinless Dirac electrons on the π-flux sqaure lattice, and analyze them by using infinite density matrix renormalization group. It is found that the diamagnetism remains intact when the short-range interaction V is weak, while it is monotonically suppressed for larger interactions. Around the quantum critical point (QCP) of a charge density wave phase transition, we find a scaling behavior of the ground state energy density characteristic of the chiral Ising universality class. This leads to universal orbital diamagnetism in correlated Dirac electrons around the QCP, which may be regarded as a quantum, magnetic analogue of critical Casimiar effect which has been widely studied for classical phase transitions.

Disentangling Orbital Magnetic Susceptibility with Wannier Functions

“…For the calculation of χ, we need Tr G as shown in Eq. (8). Now Tr G = Tr G = Tr G = Tr g + q g 1 + q 2 2 g 2 .…”

“…For instance, it can be used to detect singular band structures in solids such as Dirac electrons. [4][5][6][7][8] In theory, despite its conceptual simplicity, i.e., the magnetic susceptibility is essentially just the lowest-order magnetic moment in external magnetic field, the formula for the orbital magnetic susceptibility is very involved as shown in the early studies. [9][10][11][12][13][14][15][16] It was only when Fukuyama combined the Luttinger-Kohn representation 17) and the Green's function technique, that we had a gauge invariant compact formula for the orbital magnetic susceptibility.…”