lattice-system

Tasaki (2020), Chapter 2

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• Single-site Pauli operators
• Spin-1/2 operators (Tasaki §2.1)
• Spin-1/2 rotation operators (Tasaki §2.1 eq. (2.1.26))
• 3D rotation matrices R^(α)_θ (general θ, Tasaki §2.1 eq. (2.1.11))
• Z₂ × Z₂ representation (Tasaki §2.1 eqs. (2.1.27)-(2.1.34))
• 3D rotation matrices R^(α)_π (Tasaki §2.1 eq. (2.1.28))
• Pauli-basis decomposition (Tasaki §2.1 Problem 2.1.a, S = 1/2)
• Polynomial-basis decomposition for S = 1 (Tasaki §2.1 Problem 2.1.a, S = 1)
• S = 1 matrix representations (Tasaki §2.1 eq. (2.1.9))
• Spin-S operators (general S ≥ 0, parameterised by N = 2S : ℕ)
• Basis states and raising/lowering (Tasaki §2.1)
• Basis states and raising/lowering for S = 1 (Tasaki §2.1)
• Time-reversal map for S = 1/2 (Tasaki §2.3)
• Total spin operator (Tasaki §2.2 eq. (2.2.7), (2.2.8)) — part 1 of 5
• Total spin operator (Tasaki §2.2 eq. (2.2.7), (2.2.8)) — part 2 of 5
• Total spin operator (Tasaki §2.2 eq. (2.2.7), (2.2.8)) — part 3 of 5
• Total spin operator (Tasaki §2.2 eq. (2.2.7), (2.2.8)) — part 4 of 5
• Total spin operator (Tasaki §2.2 eq. (2.2.7), (2.2.8)) — part 5 of 5
• Two-site spin inner product (Tasaki §2.2 eq. (2.2.16))
• Spin-S Marshall–Lieb–Mattis on the magnetization sector (Tasaki §2.5 Theorem 2.2 generic S, sector form) — part 1 of 4
• Spin-S Marshall–Lieb–Mattis on the magnetization sector (Tasaki §2.5 Theorem 2.2 generic S, sector form) — part 2 of 4
• Spin-S Marshall–Lieb–Mattis on the magnetization sector (Tasaki §2.5 Theorem 2.2 generic S, sector form) — part 3 of 4
• Spin-S Marshall–Lieb–Mattis on the magnetization sector (Tasaki §2.5 Theorem 2.2 generic S, sector form) — part 4 of 4
• Spin-S saturated ferromagnetic state (Tasaki §2.4 generalised) — part 1 of 2
• Spin-S saturated ferromagnetic state (Tasaki §2.4 generalised) — part 2 of 2