Higher-order tacnodes in a free fermionic model
We investigate a one-dimensional free fermion model with nearest and next-nearest neighbor hopping, evolving in imaginary time from a product state with N consecutive fermions, and conditioned to go back to the same state after a given time. Such types of models are quantum reformulations of well-studied two-dimensional classical lattice models, which are known to give rise to limit shapes where expectation values of simple local observables, such as density, depend on position in an appropriate scaling limit. In the case of only nearest neighbor hopping, this model is known to have two fluctuating regions which can be tuned to merge depending on ratio between time and N. Correlations near the merger are governed by a so-called tacnode kernel. Here we show that another universal higher-order tacnode process can appear upon including the next-nearest neighbor term. We also discuss the limit shapes, and compute analytically the corresponding density profile.