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

TL;DR

This paper investigates the universal behavior of orbital diamagnetism in correlated Dirac fermions near a quantum critical point, revealing a scaling law characteristic of the chiral Ising universality class.

Contribution

It introduces a detailed analysis of orbital diamagnetism in a Dirac fermion system with a quantum phase transition, highlighting a universal scaling behavior at the critical point.

Findings

Diamagnetism remains robust in the Dirac semimetal phase due to competition between Fermi velocity and magnetic gap.

Diamagnetism is suppressed monotonically in the charge density wave phase.

A universal scaling behavior of diamagnetism is observed at the quantum critical point.

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 $\pi$-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 as a result of a non-trivial competition between the enhanced Fermi velocity and magnetic-field-induced mass gap, while it is monotonically suppressed in the CDW regime. Around the quantum critical point (QCP) of the CDW phase transition, we find a scaling behavior of the diamagnetism characteristic of the chiral Ising universality class. This defines a universal behavior of orbital diamagnetism in correlated Dirac fermions around a QCP, and therefore the robust diamagnetism in the semimetal regime is a universal property of Dirac systems whose criticality belongs to the chiral Ising universality class. 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.