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https://repositorio.ufrn.br/handle/123456789/30311| Title: | Emptiness formation probability and PainlevéV equation in the XY spin chain |
| Authors: | Ares, Filiberto Viti, Jacopo |
| Keywords: | Conformal field theory;Integrable spin chains and vertex models;Painlevé equations;Spin chains;ladders and planes |
| Issue Date: | 20-Jan-2020 |
| Publisher: | IOP Publishing Ltd and SISSA Medialab srl |
| Citation: | ARES, Filiberto; VITI, Jacopo. Emptiness formation probability and Painlevé V equation in the XY spin chain. Journal Of Statistical Mechanics: Theory and Experiment, [S.L.], v. 2020, n. 1, p. 013105, 20 jan. 2020. Disponível em: https://iopscience.iop.org/article/10.1088/1742-5468/ab5d0b. Acesso em: 11 ago. 2020. http://dx.doi.org/10.1088/1742-5468/ab5d0b |
| Portuguese Abstract: | We reconsider the problem of finding Lconsecutive 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 o-critical behaviour of the emptiness formation probability is exactly described by a τfunction of a PainlevéV equation. Following a recent proposal, we also provide a power series expansion for the τfunction 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 |
| URI: | https://repositorio.ufrn.br/handle/123456789/30311 |
| ISSN: | 1742-5468 |
| Appears in Collections: | ECT - Artigos publicados em periódicos |
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