Possible ground state wavefunctions of anti-ferromagnetic Heisenberg spin chains

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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?

This post imported from StackExchange Physics at 2020-11-09 09:42 (UTC), posted by SE-user annie marie heart
asked Nov 3, 2018
retagged Nov 9, 2020
Which spin - spin 1/2, spin 1, ... ?

This post imported from StackExchange Physics at 2020-11-09 09:42 (UTC), posted by SE-user Norbert Schuch
@Nobert Both cases, spin 1/2 and spin 1

This post imported from StackExchange Physics at 2020-11-09 09:42 (UTC), posted by SE-user annie marie heart
You are aware that the physics of integer and half-integer Heisenberg chains is fundamentally different?

This post imported from StackExchange Physics at 2020-11-09 09:42 (UTC), posted by SE-user Norbert Schuch
Yes. Spin-1/2: One is gapless like O(3) NLSM. Spin-1: The other is gapped, either trivial or Haldane phase.

This post imported from StackExchange Physics at 2020-11-09 09:42 (UTC), posted by SE-user annie marie heart
Wonder how to view the wavefunction.

This post imported from StackExchange Physics at 2020-11-09 09:42 (UTC), posted by SE-user annie marie heart
@Norbert Schuch I post a new question maybe you also know it -- a lattice model

This post imported from StackExchange Physics at 2020-11-09 09:42 (UTC), posted by SE-user annie marie heart

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