Emptiness formation probability and Painlevé V equation in the XY spin chain

DOI10.1088/1742-5468/AB5D0BzbMATH Open1459.82063arXiv1909.01270OpenAlexW2971467807MaRDI QIDQ5856219

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Publication date: 25 March 2021

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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 $au$ function of a Painlev'e V equation. Following a recent proposal, we also provide a power series expansion for the $au$ 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 rediscuss the free fermion case where the Emptiness Formation Probability is characterized by a Gaussian decay for large $L$.

Full work available at URL: https://arxiv.org/abs/1909.01270

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