Nonequilibrium from Equilibrium: Chiral Current-Carrying States in the Spin-1 Babujian-Takhtajan Chain
We study the spin-$1$ Babujian-Takhtajan chain deformed by its third conserved charge $Q_3$. We derive $Q_3$ and show that it is a dimensionless energy current and that its local density is a dressed scalar-chirality operator rather than bare chirality alone, as is the case for the spin-$1/2$ Heisenberg chain. The deformation $H_α=H+αQ_3$ therefore provides a local, exactly solvable current bias: it leaves the eigenstates of the original Hamiltonian unchanged, but reorders them so that selected high-energy current-carrying states become ground states of the tilted problem. Using the thermodynamic Bethe ansatz and confirming the analytical calculations with DMRG, we find a quantum phase transition at $α_c={J}/(8π)$. For $α<α_c$, the ground-state remains the undeformed Babujian-Takhtajan phase whose low-energy effective field theory is described by the $SU(2)$ Wess-Zumino-Witten (WZW) model at level $k=2$ representing a critical phase characterized by a central charge $c=3/2$ and $\langle Q_3\rangle=0$. For $α>α_c$, a finite rapidity interval forms, and the system enters a gapless chiral current-carrying sector described by a $c=3/2$ CFT. Near the threshold, the free energy starts quadratically as a function of $α-α_c$, while the energy current turn on linearly. The scalar chirality turns on at the same threshold, showing that the postcritical sector is simultaneously current-carrying and chiral. The most immediate experimental routes are composite spin-1 bosons in optical lattices, and programmable qutrit simulators based on trapped ions or superconducting circuits.