2025/11/27 by Xu, Xia-Ze, Lin, Tong-Yu, Zhang, Guang-Ming
Materials Science · Physics and Astronomy · #FOS: Physical sciences #Material Dynamics and Properties #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics
paper · doi:10.48550/arxiv.2511.22477
openalex publication_date 2025/11/27 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28
The long-standing question of whether the residual entropy of hexagonal ice (Sh) equals that of cubic ice (Sc) remains unresolved despite decades of research on ice-type models. While analytical studies have established the inequality Sh ≥ Sc, numerical investigations suggest that the two values are very close. In this work, we revisit this problem using high-precision tensor-network methods. In Monte Carlo approaches the residual entropy cannot be directly obtained by sampling the ground-state degeneracy space, however, the tensor-network framework enables an explicit encoding of the "ice rule'' into local tensors, and then the residual entropy is transformed into finding the largest eigenvalue of a transfer operator in the form of a projected entangled-pair operator, which allows high-accuracy numerical evaluation. Meanwhile, we propose a new perspective based on analyzing the normality of the transfer operator, and demonstrate that if the operator is normal, the equality Sh = Sc follows directly. Then the variational tensor network methods are employed to numerically verify this normality. Finally both residual entropies are directly computed by using our recently developed split corner transfer matrix renormalization group algorithm, providing a rigorous evidence supporting the equality between Sh and Sc.