We investigate the entanglement properties of the Quantum Six-Vertex Model on a cylinder, focusing on the Shannon-Rényi entropy in the limit of Rényi order $n=\infty$. This entropy, calculated from the ground state amplitudes of the equivalent XXZ spin-1/2 chain, allows us to determine the Renyi entanglement entropy of the corresponding Rokhsar-Kivelson wave functions, which describe the ground states of certain conformal quantum critical points. Our analysis reveals a logarithmic correction to the expected entanglement scaling when the system size is odd. This anomaly arises from the geometric frustration of spin configurations imposed by periodic boundary conditions on odd-sized chains. We demonstrate that the scaling prefactor of this logarithmic term is directly related to the compactification radius of the low-energy bosonic field theory description or, equivalently, the Luttinger parameter. Thus, this correction directly probes the underlying Conformal Field Theory describing the critical point. Our findings highlight the crucial role of system size parity in determining this model's entanglement properties and offer insights into the interplay between geometry, frustration, and criticality.

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• Conformal field theory
• Entanglement entropy
• Quantum criticality
• Quantum entanglement
• Shannon entropy
• Conformal symmetry
• Exact diagonalization
• Heisenberg model
• Luttinger liquid model
• Spin chains
• XYZ model