Nonequilibrium from Equilibrium: Chiral Current-Carrying States in the Spin-1 Babujian-Takhtajan Chain

TL;DR

This paper investigates how a specific deformation of the spin-1 Babujian-Takhtajan chain induces a quantum phase transition to a chiral current-carrying phase, combining analytical and numerical methods to characterize the transition.

Contribution

It introduces a local, exactly solvable current bias via the third conserved charge, revealing a phase transition to a chiral current-carrying state in the spin-1 chain.

Findings

Identifies a quantum phase transition at a critical deformation parameter.

Describes the critical phase with a $c=3/2$ conformal field theory.

Shows the scalar chirality and energy current activate simultaneously at the transition.

Abstract

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 $H_\alpha=H+\alpha Q_3$ 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 $\alpha_c={J}/(8\pi)$. For $\alpha<\alpha_c$, 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 $\alpha>\alpha_c$, 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 $\alpha-\alpha_c$, 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.