Interface fluctuations associated with split Fermi seas

Abstract

We consider the asymptotic behaviour of a family of unidimensional lattice fermion models, which are in exact correspondence with certain probability laws on partitions and on unitary matrices. These models exhibit limit shapes, and in the case where the bulk of these shapes are described by analytic functions, the fluctuations around their interfaces have been shown to follow a universal Tracy-Widom distribution or its higher-order analogue. Non-differentiable bulk limit shape functions arise when a gap appears in some quantum numbers of the model, in other words when the Fermi sea is split. We show that split Fermi seas give rise to new interface fluctuations, governed by integer powers of universal distributions. This breakdown in universality is analogous to the behaviour of a random Hermitian matrix when the support of its limiting eigenvalue distribution has multiple cuts, with oscillations appearing in the limit of the two-point correlation function. We show that when the Fermi sea is split in the lattice fermion model, there are multiple cuts in the eigenvalue support of the corresponding unitary matrix model.

arXiv comment24 pages, 3 figures; v2: final version

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• Multicritical Schur measures and higher-order analogues of the Tracy-Widom distribution