Four-spin-exchange- and magnetic-field-induced chiral order in two-leg spin ladders

Abstract

We propose a mechanism of a vector chiral long-range order in two-leg spin-$\frac{1}{2}$ and spin-1 antiferromagnetic ladders with four-spin exchanges and a Zeeman term. It is known that for one-dimensional quantum systems, spontaneous breakdown of continuous symmetries is generally forbidden. Any vector chiral order hence does not appear in spin-rotationally [SU(2)]-symmetric spin ladders. However, if a magnetic field is added along the ${S}^{z}$ axis of ladders and the SU(2) symmetry is reduced to the U(1) one, the $z$ component of a vector chiral order can emerge with the remaining U(1) symmetry unbroken. Making use of Abelian bosonization techniques, we actually show that a certain type of four-spin exchange can yield a vector chiral long-range order in spin-$\frac{1}{2}$ and spin-1 ladders under a magnetic field. In the chiral-ordered phase, the ${Z}_{2}$ interchain-parity (i.e., chain-exchange) symmetry is spontaneously broken. We also consider effects of perturbations breaking the parity symmetry.