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In this paper we explore the properties of a 1-dimensional spin chain in thepresence of chiral interactions, focusing on the system's transition todistinct chiral phases for various values of the chiral coupling. By employingthe mean field theory approximation we establish a connection between thischiral system and a Dirac particle in the curved spacetime of a black hole.Surprisingly, the black hole horizon coincides with the interface betweendistinct chiral phases. We examine the chiral properties of the system forhomogeneous couplings and in scenarios involving position dependent couplingsthat correspond to black hole geometries. To determine the significance ofinteractions in the chiral chain we employ bosonization techniques and derivethe corresponding Luttinger liquid model. Furthermore, we investigate theclassical version of the model to understand the impact of the chiral operatoron the spins and gain insight into the observed chirality. Our findings shedlight on the behavior of the spin chain under the influence of the chiraloperator, elucidating the implications of chirality in various contexts,including black hole physics.

Exploring interacting chiral spin chains in terms of black hole physics