  In the presence of non-Hermitian skin effect, non-Hermitian lattices
generally have complex-valued eigenenergies under periodic boundary condition,
but they can have non-Bloch PT symmetry and therefore completely real
eigenenergies under open boundary condition. This novel PT symmetry and its
breaking have been experimentally observed in one dimension. Here, we find that
non-Bloch PT symmetry in two and higher dimensions exhibits drastically
different behaviors compared to its one-dimensional counterpart. Whereas Bloch
PT breaking and one-dimensional non-Bloch PT breaking generally have nonzero
thresholds in the large-size limit, the threshold of two and higher-dimensional
non-Bloch PT breaking universally approaches zero as the system size increases.
A product measure, namely the product of bare non-Hermiticity and system size,
is introduced to quantify the PT breaking tendency. This product being small is
required for the perturbation theory to be valid, thus its growth with system
size causes the breakdown of perturbation theory, which underlies the universal
threshold. That the universal behaviors emerge only in two and higher
dimensions indicates an unexpected interplay among PT symmetry, non-Hermitian
skin effect, and spatial dimensionality. Our predictions can be confirmed on
experimentally accessible platforms.
