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

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.

10 pages

References in corpus (21)

• The density-matrix renormalization group in the age of matrix product states
• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• Interactions and phase transitions on graphene's honeycomb lattice
• Theory of interacting electrons on the honeycomb lattice
• Quantum Hall effect in a bulk antiferromagnet EuMnBi${}_2$ with magnetically confined two-dimensional Dirac fermions
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• The Casimir effect: from quantum to critical fluctuations
• Transport Properties and Diamagnetism of Dirac Electrons in Bismuth
• Universal scaling functions of critical Casimir forces obtained by Monte Carlo simulations
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• Anomalous Orbital Magnetism and Hall Effect of Massless Fermions in Two Dimension
• Diamagnetism in disordered graphene
• Many-body orbital paramagnetism in doped graphene sheets
• Aspect-ratio dependence of thermodynamic Casimir forces
• Diamagnetism of doped two-leg ladders and probing the nature of their commensurate phases
• Diamagnetism of nodal fermions
• Giant orbital diamagnetism of three-dimensional Dirac electrons in Sr${}_3$PbO antiperovskite
• Quantum Phase Transition in Organic Massless Dirac Fermion System $\alpha$-(BEDT-TTF)${}_2$I${}_3$ under pressure
• Comment on "The role of electron-electron interactions in two-dimensional Dirac fermions''
• Local Observations of Orbital Diamagnetism and Excitation in Three-Dimensional Dirac Fermion Systems Bi${}_{1-x}$Sb${}_x$
• Response to Comment on "The role of electron-electron interactions in two-dimensional Dirac fermions"