  Recently, the subradiant states of one-dimensional two-level atom chains
coupled to light modes were found to have decay rates obeying a universal
scaling, and an unexpected fermionic character of the multiply-excited
subradiant states was discovered. In this Letter, we theoretically obtain the
singly-excited subradiant states, and by eliminating the superradiant modes, we
demonstrate a relation between the multiply-excited subradiant states and the
Tonks-Girardeau limit of the Lieb-Liniger model which explains the fermionic
behavior. In addition, we identify a new family of states with correlations
different from the fermionic ansatz.
