lattice-system

Legacy catalogue: Single-site Pauli operators

Interim authority. This lossless catalogue chunk remains authoritative for formalization status and capstone identification until Issue #5228. The version 1 JSON catalogue is still a non-authoritative prototype.

Interim catalogueSpin foundations and Tasaki Chapter 2

Single-site Pauli operators

Primary reference: Tasaki, Physics and Mathematics of Quantum Many-Body Systems, §2.1 eq. (2.1.8), p. 15. Cross-checked with Nielsen-Chuang §2.1.3 Figure 2.2 (pp. 65-66, definitions), Ex. 2.19 (p. 70, Hermiticity), Ex. 2.41 (p. 78, (σ^α)² = I and anticommutation), Ex. 2.40 (p. 77, commutator, whence the cyclic products).

Lean name Statement File
pauliX/Y/Z_isHermitian (σ^α)† = σ^α Quantum/Pauli.lean
pauliX/Y/Z_mul_self (σ^α)² = I Quantum/Pauli.lean
pauliX_mul_pauliY etc. σ^x σ^y = i·σ^z (cyclic) Quantum/Pauli.lean
pauliX_anticomm_pauliY etc. σ^α σ^β + σ^β σ^α = 0 (α ≠ β) Quantum/Pauli.lean

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