  We study the low-energy properties of the one-dimensional spin-1/2 XXZ chain
with time-reversal symmetry-breaking pseudo-scalar chiral interaction and
propose a phase diagram for the model. In the integrable case of the isotropic
Heisenberg model with the chiral interaction, we employ the thermodynamic Bethe
ansatz to find "chiralization", the response of the ground state versus the
strength of the pseudo-scalar chiral interaction of a chiral Heisenberg chain.
Unlike the magnetization case, the chirality of the ground state remains zero
until the transition point corresponding to critical coupling $\alpha_c=2J/\pi$
with $J$ being the antiferromagnetic spin-exchange interaction. The
central-charge $c=1$ conformal field theories (CFTs) describe the two phases
with zero and finite chirality. We show for this particular case and conjecture
more generally for similar phase transitions that the difference between two
emergent CFTs with identical central charges lies in the symmetry of their
ground state (lightest weight) primary fields, i.e., the two phases are
symmetry-enriched CFTs. At finite but small temperatures, the non-chiral
Heisenberg phase acquires a finite chirality that scales with the temperature
quadratically. We show that the finite-size effect around the transition point
probes the transition.
