Yukawa-Lorentz symmetry of interacting non-Hermitian birefringent Dirac fermions

TL;DR

This paper explores non-Hermitian birefringent Dirac fermions, revealing how interactions can lead to emergent Lorentz symmetry and novel quantum critical states in a lattice model.

Contribution

It introduces a non-Hermitian generalization of birefringent Dirac fermions and shows how interactions induce emergent Lorentz symmetry and quantum criticality.

Findings

Real eigenvalue spectra in extended NH parameter regimes

Interaction-driven vanishing birefringence at criticality

Emergent Lorentz symmetry with a shared Fermi velocity

Abstract

The energy spectra of linearly dispersing gapless spin-3/2 Dirac fermions display birefringence, featuring two effective Fermi velocities, thus breaking the space-time Lorentz symmetry. Here, we consider a non-Hermitian (NH) generalization of this scenario by introducing a masslike anti-Hermitian birefringent Dirac operator to its Hermitian counterpart. At the microscopic level, a generalized $\pi$-flux square lattice model with imbalance in the hopping amplitudes in the opposite directions among spinless fermions between the nearest-neighbor sites gives rise to pseudospin-3/2 NH Dirac fermions in terms of internal, namely sublattice, degrees of freedom. The resulting NH operator shows real eigenvalue spectra over an extended NH parameter regime, and a combination of non-spatial and discrete rotational symmetries protects the gapless nature of such quasiparticles. However, at the brink of dynamic mass generation, triggered by Hubbardlike local interactions, the birefringent parameter always vanishes under coarse grain due to the Yukawa-type interactions with scalar bosonic order-parameter fluctuations. The resulting quantum critical state is, therefore, described by two decoupled copies of spin-1/2 Dirac fermions with a unique terminal Fermi velocity, which is equal to the bosonic order-parameter velocity, thereby fostering an emergent space-time Lorentz symmetry. Furthermore, depending on the internal algebra between the anti-Hermitian birefringent Dirac operator and the candidate mass order, the system achieves the emergent Yukawa-Lorentz symmetry either by maintaining its non-Hermiticity or by recovering a full Hermiticity. We discuss the resulting quantum critical phenomena and possible microscopic realizations of the proposed scenarios.