  We investigate the steady-state and dynamical properties of a reciprocal
many-body system consisting of self-propelled active particles with local
alignment interactions that exists within a fan-shaped neighborhood of each
particle. We find that the nonreciprocity can emerge in this reciprocal system
once the spontaneous symmetry breaking is present, and the effective
description of the system assumes a non-Hermitian structure that directly
originates from the emergent nonreciprocity. This emergent nonreciprocity can
impose strong influences on the properties the system. In particular, it can
even drive a real-space condensation of active particles. Our findings pave the
way for identifying a new class of physics in reciprocal systems that is driven
by the emergent nonreciprocity.
