Note on searching for critical lattice models as entropy critical points from strange correlator

An entropy function is proposed in [T. C. Lin and J. McGreevy, Phys. Rev. Lett. 131, 251602 (2023)] as a way to detect criticality even when the system size is small. In this note we apply this strategy in the search for criticality of lattice transfer matrices constructed based on the topological holographic principle. We find that the combination of strategy is indeed a cost-effective and efficient way of identifying critical boundary conditions, estimating central charges and moreover, plotting entire phase diagrams in a multi-dimensional phase space.