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Ah, but who says that negative absolute temperatures exist at all? This is not without its controversies. There's a nature paper here which challenges the very existence of negative absolute temperatures, arguing that negative temperatures come about due to a poor method of defining the entropy, which in turn is used to calculate the temperature. Other ...


It is correct that if you proceed the way you describe it, you obtain a 4-local parent Hamiltonian $H=\sum h$, where $h\ge0$, and $h\vert\Psi\rangle=0$, where $\vert\Psi\rangle$ is the AKLT state. For a parent Hamiltonian constructed this way, one can show (for an arbitrary injective MPS) that the ground state is unique with a gap above. However, if you ...

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