  An understanding of the possible ways in which interactions can produce
fundamentally new emergent many-body states is a central problem of condensed
matter physics. We ask if a Fermi sea can arise in a system of bosons subject
to contact interaction. Based on exact diagonalization studies and variational
wave functions, we predict that such a state is likely to occur when a system
of two-component bosons in two dimensions, interacting via a species
independent contact interaction, is exposed to a synthetic magnetic field of
strength that corresponds to a filling factor of unity. The fermions forming
the SU(2) singlet Fermi sea are bound states of bosons and quantized vortices,
formed as a result of the repulsive interaction between bosons in the lowest
Landau level.
