Fermionic Gaussian pure state amplitudes in arbitrary local Pauli bases are given by an explicit Pfaffian formula plus a recursion for different qubit counts.
Correlation Function of the Spin-1/2 XXX Antiferromagnet
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We consider a special correlation function in the isotropic spin-$\half$ Heisenberg antiferromagnet. It is the probability of finding a ferromagnetic string of (adjacent) spins in the antiferromagnetic ground state. We give two different representations for this correlation function. Both of them are exact at any distance, but one becomes more effective for the description of long distance behaviour, the other for the description of short distance behaviour.
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Explicit Pfaffian Formula for Amplitudes of Fermionic Gaussian Pure States in Arbitrary Pauli Bases
Fermionic Gaussian pure state amplitudes in arbitrary local Pauli bases are given by an explicit Pfaffian formula plus a recursion for different qubit counts.