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Unveiling chiral phases: Finite-size scaling as a probe of quantum phase transition in symmetry-enriched $c=1$ conformal field theories. (arXiv:2312.16660v2 [cond-mat.str-el] UPDATED)

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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 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.

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