Abstract
We reconsider the problem of finding L consecutive down spins in the ground state of the XY chain, a quantity known as the Emptiness Formation Probability. Motivated by new developments in the asymptotics of Toeplitz determinants, we show how the crossover between the critical and off-critical behaviour of the emptiness formation probability is exactly described by a function of a Painlevé V equation. Following a recent proposal, we also provide a power series expansion for the function in terms of irregular conformal blocks of a conformal field theory with central charge c = 1. Our results are tested against lattice numerical calculations, showing excellent agreement. We finally discuss the free fermion case where the emptiness formation probability is characterized by a Gaussian decay for large L.
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