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This preprint advances the theoretical understanding of random tensor networks by utilizing star-triangle duality to precisely estimate critical bond dimensions on triangular and honeycomb lattices. By treating a star-triangle block as the fundamental unit rather than an individual bond, the study offers new insights into entanglement regimes relevant to quantum many-body systems and condensed matter physics.

Source coveringQuantum Zeitgeist

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Triangular Lattice Estimate Reaches 1.475661534848 Via Duality

Quantum ZeitgeistAugust 19, 20263 min read

The analysis estimates the critical bond dimension for the honeycomb lattice to be 2.634929344884, and the associated single-bond duality relation yields the triangular-lattice estimate 1.475661534848. This calculation uses star-triangle duality with symmetric-group permutation models on triangular and honeycomb lattices.

Masayuki Ohzeki of the Tohoku University has developed a new method for estimating the critical bond dimensions of random tensor networks on triangular and honeycomb lattices by applying star-triangle duality to permutation models. The approach, described in a recent preprint, departs from conventional duality analyses by treating…

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