Finite-size effect explanation for entropy–central-charge mismatch in A6 and A7

Determine whether the observed discrepancy between the entropy function maximum SΔ and one third of the central charge for the strange-correlator constructions using input categories A6 and A7 is caused by finite-size effects that become prominent at high bond dimensions. Specifically, analyze the dependence of SΔ on system size and bond dimension for the four-site circular transfer-matrix ground states constructed from competing condensates between Frobenius algebras 0 and 0 ⊕ 2 in A-series models, and establish whether this finite-size effect accounts for the mismatch.

Background

The paper employs the entropy function criterion of Lin and McGreevy to identify critical points and estimate central charges from small lattices constructed via the strange correlator. For four equally spaced sites on a circle, the cross-ratio is 1/2, and the entropy identity predicts SΔ = c/3 at criticality.

In the A-series tests (input categories A3–A7), the entropy function exhibits clear peaks near predicted critical couplings, and for A3–A5, the maxima closely match c/3. However, for A6 and A7, the maxima deviate from c/3. The authors explicitly conjecture that this deviation is due to finite-size effects being prominent at high bond dimensions, suggesting an unresolved question regarding the cause of the mismatch.