We show that scalar chiral order can be induced by four-spin exchanges in the two-leg spin ladder, using the spin-chirality duality transformation and matrix-product ansatz. Scalar-chiral-ordered states are found to be exact ground states in a family of spin ladder models. In this scalar chiral phase, there is a finite energy gap above the doubly degenerate ground states and a ${Z}_{2}\ifmmode\times\else\texttimes\fi{}{Z}_{2}\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ symmetry is fully broken. It is also shown that the SU(4)-symmetric model, which is self-dual under the duality transformation, is on a multicritical point surrounded by the staggered dimer phase, the staggered scalar chiral phase, and the gapless phase.We show that scalar chiral order can be induced by four-spin exchanges in the two-leg spin ladder, using the spin-chirality duality transformation and matrix-product ansatz. Scalar-chiral-ordered states are found to be exact ground states in a family of spin ladder models. In this scalar chiral phase, there is a finite energy gap above the doubly degenerate ground states and a ${Z}_{2}\ifmmode\times\else\texttimes\fi{}{Z}_{2}\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ symmetry is fully broken. It is also shown that the SU(4)-symmetric model, which is self-dual under the duality transformation, is on a multicritical point surrounded by the staggered dimer phase, the staggered scalar chiral phase, and the gapless phase.

arXiv:cond-mat/0304106Physical review. B, Condensed matterMay 16, 200334 citations

Field-induced chirality in a frustrated quantum spin ladder

M. Pikulski

Jan 1, 20171 citation

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

Masahiro Sato

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.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.

arXiv:cond-mat/0703396Physical Review BAug 14, 200715 citations

Dynamics in a two-leg spin ladder with a four-spin cyclic interaction

Satoshi Nishimoto, Mitsuhiro Arikawa

We study the two-leg Heisenberg ladder with four-spin cyclic interaction using the (dynamical) density-matrix renormalization-group method. We demonstrate the dependence of the low-lying excitations in the spin wave, staggered dimer order, and scalar-chirality order structure factors on the four-spin cyclic interaction. We find that the cyclic interaction enhances spin-spin correlations with wave vector around momentum $({q}_{x},{q}_{y})=(\frac{\ensuremath{\pi}}{2},0)$. Also, the presence of long-range order in the staggered dimer and scalar-chirality phases is confirmed by a $\ensuremath{\delta}$-function peak contribution of the structure factors at energy $\ensuremath{\omega}=0$.We study the two-leg Heisenberg ladder with four-spin cyclic interaction using the (dynamical) density-matrix renormalization-group method. We demonstrate the dependence of the low-lying excitations in the spin wave, staggered dimer order, and scalar-chirality order structure factors on the four-spin cyclic interaction. We find that the cyclic interaction enhances spin-spin correlations with wave vector around momentum $({q}_{x},{q}_{y})=(\frac{\ensuremath{\pi}}{2},0)$. Also, the presence of long-range order in the staggered dimer and scalar-chirality phases is confirmed by a $\ensuremath{\delta}$-function peak contribution of the structure factors at energy $\ensuremath{\omega}=0$.

arXiv:0811.2456Physical Review BMar 27, 20099 citations

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.