# Possible ground state wavefunctions of anti-ferromagnetic Heisenberg spin chains

1. What are the ground state wavefunctions of the anti-ferromagnetic (AFM) Heisenberg spin chains?

Is that which of the following? $$| ↑↓↑↓ · · · ↑↓>$$ or $$| ↓↑↓↑ . . . ↓↑>$$ or $$| ↑↓↑↓ · · · ↑↓> +| ↓↑↓↑ . . . ↓↑>$$ or $$| ↑↓↑↓ · · · ↑↓> - | ↓↑↓↑ . . . ↓↑>$$

1. What are the number of ground states?

2. What are the Neel states?

• Which spin - spin 1/2, spin 1, ... ? – Norbert Schuch Nov 8 '18 at 21:10
• @Nobert Both cases, spin 1/2 and spin 1 – annie marie heart Dec 30 '18 at 0:25
• You are aware that the physics of integer and half-integer Heisenberg chains is fundamentally different? – Norbert Schuch Dec 30 '18 at 0:27
• Yes. Spin-1/2: One is gapless like O(3) NLSM. Spin-1: The other is gapped, either trivial or Haldane phase. – annie marie heart Dec 30 '18 at 0:30
• Wonder how to view the wavefunction. – annie marie heart Dec 30 '18 at 0:30