Every matrix element of a fermionic Gaussian operator between arbitrary Pauli product states is expressed as a single Pfaffian of a 2L by 2L kernel with explicitly tabulated sign matrices.
Emptiness Formation Probability for the One-Dimensional Isotropic XY Model
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abstract
We study a correlation function for the one-dimensional isotropic ${XY}$ model (${XX0}$ model), which is called the Emptiness Formation Probability (EFP). It is the probability of the formation of a ferromagnetic string in the anti-ferromagnetic ground state. Using the expression of the EFP as a Toeplitz determinant, we discuss its asymptotic behaviors. We also compare the analytical results with numerical calculations as the density-matrix renormalization group and the quantum Monte-Carlo method.
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Matrix Elements of Fermionic Gaussian Operators in Arbitrary Pauli Bases: A Pfaffian Formula
Every matrix element of a fermionic Gaussian operator between arbitrary Pauli product states is expressed as a single Pfaffian of a 2L by 2L kernel with explicitly tabulated sign matrices.