$\mathcal{P}\mathcal{T}$-symmetry as Effective Time Reversal Symmetry for Anderson Localization in a Collinear Antiferromagnet

We show that $\mathcal{P}\mathcal{T}$-symmetry acts as the effective time-reversal symmetry governing Anderson localization in the antiferromagnet BaMn${}_2$Bi${}_2$, whereas the general time-reversal symmetry is broken by its long-range magnetic order. The magnetoconductance follows the laws established from breaking time-reversal symmetry throuhg the orbital coupling of charge carriers to the magnet vector potential, however, the degrees of symmetry breaking are qualitatively modulated by the magnetocrystalline anisotropy stabilizing $\mathcal{P}\mathcal{T}$-related sublattices. The quantum interferences and hoping amplitudes governing the phenomena are drastically impaired by transverse magnetic fields, which readily cant $\mathcal{P}\mathcal{T}$-related magnetic sublattices. Accordingly, when the $\mathcal{P}\mathcal{T}$-related texture is weakly perturbed by longitudinal fields orienting along the sublattices, the localization is minutely affected. The robustness of the $\mathcal{P}\mathcal{T}$-enforced degeneracies is thus governed by exchange and magnetocrystalline interactions, in contrast to the exact $\mathcal{P}\mathcal{T}$-symmetry of the full Hamiltonian, which is broken by any finite field.