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We study the low-energy properties of the one-dimensional spin-1/2 XXZ chainwith time-reversal symmetry-breaking pseudo-scalar chiral interaction andpropose a phase diagram for the model. In the integrable case of the isotropicHeisenberg model with the chiral interaction, we employ the thermodynamic Betheansatz to find "chiralization", the response of the ground state versus thestrength of the chiral interaction of a chiral Heisenberg chain. Unlike themagnetization case, the chirality of the ground state remains zero until thetransition 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 finitechirality. We show for this particular case and conjecture more generally forsimilar phase transitions that the difference between two emergent CFTs withidentical central charges lies in the symmetry of their ground state (lightestweight) primary fields, i.e., the two phases are symmetry-enriched CFTs. Atfinite but small temperatures, the non-chiral Heisenberg phase acquires afinite chirality that scales with the temperature quadratically. We show thatthe finite-size effect around the transition point probes the transition.

Unveiling chiral phases: Finite-size scaling as a probe of quantum phase transition in symmetry-enriched $c=1$ conformal field theories