Phases and phase transitions in the chiral Babujian-Takhtajan chain

The quantum Babujian-Takhtajan (BT) model generalizes the integrable S=1/2 Heisenberg chain to higher spins. One key characteristic of integrable models is the existence of infinitely many conserved quantities for infinitely large systems. We examine the phases and phase transitions in the S=1 BT model with a chiral term by first constructing the conserved quantities, noting that one of them is the chiral term with an additional irrelevant operator: $\hat{Q} =\hat{\chi}+\hat{Q}_{\text{irrelevant}}$, where $\hat\chi=\sum_{i=1}^{\infty}{\bf S}_i({\bf S}_{i+1}\times{\bf S}_{i+2})$ . Using the thermodynamic Bethe ansatz, we derive the free energy of the model associated with the BT Hamiltonian, $H_{\text{BT}}$, with an added term: $\alpha \hat{Q}$. We demonstrate the existence of a critical value $\alpha_c$ such that for $\alpha>\alpha_c$ the ground state becomes gapless and chiral, with a finite expectation value of the chirality operator $\langle {\bf S}_i{({\bf S}_{i+1}\times{\bf S}_{i+2}}) \rangle$ and $\langle \hat{Q}_{\text{irrelevant}} \rangle =0$. We calculate the entanglement entropy in the chiral phase and find that it corresponds to a $c=3/2$ CFT, which differs from the CFT of the BT model: the SU(2) WZNW model at level 2. Our analytical results are validated through DMRG simulations.