Berezinskii-Kosterlitz-Thouless-like localization-localization transitions in disordered two-dimensional quantized quadrupole insulators

Anderson localization transitions are usually referred to as disorder-driven quantum phase transitions from delocalized states to localized states. Here we report an unconventional "Anderson localization transition" in two-dimensional quantized quadrupole insulators. Such transitions are from symmetry-protected topological corner states to disorder-induced normal Anderson localized states, which can occur in the bulk as well as on the boundary. We show that these localization-localization transitions (transitions between two different types of localized states) can happen in both Hermitian and non-Hermitian quantized quadrupole insulators and investigate their criticality by finite-size scaling analysis of the corner density. The scaling analysis suggests that the correlation length of the phase transition, on the Anderson insulator side and near critical disorder W_c, diverges as ξ (W ) ∝exp[α /√{|W − W_c| }] , a typical feature of Berezinskii-Kosterlitz-Thouless-like transitions.