arXiv:1204.0333 · Physical Review B

Semiclassical approach to competing orders in a two-leg spin ladder with ring exchange

Kiyohito Totsuka, P. Lecheminant, Sylvain Capponi

Published Jul 30, 2012• 17 citations

Abstract

We investigate the competition between different orders in the two-leg spin ladder with a ring-exchange interaction by means of a bosonic approach. The latter is defined in terms of spin-1 hard-core bosons which treat the N\'eel and vector-chirality order parameters on an equal footing. A semiclassical approach of the resulting model describes the phases of the two-leg spin ladder with a ring exchange. In particular, we derive the low-energy effective actions which govern the physical properties of the rung-singlet and dominant vector-chirality phases. As a by-product of our approach, we reveal the mutual induction phenomenon between spin and chirality with, for instance, the emergence of a vector-chirality phase from the application of a magnetic field in bilayer systems coupled by four-spin exchange interactions.

DOI: 10.1103/physrevb.86.014435

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arXiv:1204.0333 · Physical Review B

Semiclassical approach to competing orders in a two-leg spin ladder with ring exchange

Kiyohito Totsuka, P. Lecheminant, Sylvain Capponi

Published Jul 30, 2012• 17 citations

arXiv HTML PDF

Abstract

We investigate the competition between different orders in the two-leg spin ladder with a ring-exchange interaction by means of a bosonic approach. The latter is defined in terms of spin-1 hard-core bosons which treat the N'eel and vector-chirality order parameters on an equal footing. A semiclassical approach of the resulting model describes the phases of the two-leg spin ladder with a ring exchange. In particular, we derive the low-energy effective actions which govern the physical properties of the rung-singlet and dominant vector-chirality phases. As a by-product of our approach, we reveal the mutual induction phenomenon between spin and chirality with, for instance, the emergence of a vector-chirality phase from the application of a magnetic field in bilayer systems coupled by four-spin exchange interactions.

DOI: 10.1103/physrevb.86.014435

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Phase diagram of a spin-1/2 Heisenberg ladder with a chirality-chirality interaction

Matéo Fontaine, Shunsuke Furukawa

A spin-1/2 Heisenberg model with a chirality-chirality interaction (CCI) on a two-leg ladder provides a minimal setup to explore an interplay between spin and chirality degrees of freedom. This model is potentially relevant for understanding the effects of a four-spin ring exchange and a phonon-mediated interaction on a ladder. By applying the Abelian bosonization and two types of spin-chirality duality, we derive a comprehensive ground-state phase diagram that includes previously unexplored cases of a ferromagnetic rung exchange $J_\perp<0$ or a negative CCI $K_{\rm ch}<0$ . The phase diagram consists of the rung singlet (RS) phase, the Haldane phase, and three non-magnetic ordered phases. Moreover, the RS and Haldane phases consist of several regions with different dominant correlations in terms of spin, dimer, or chirality. We perform numerical simulations to confirm the predicted phase structure and critical properties.A spin-1/2 Heisenberg model with a chirality-chirality interaction (CCI) on a two-leg ladder provides a minimal setup to explore an interplay between spin and chirality degrees of freedom. This model is potentially relevant for understanding the effects of a four-spin ring exchange and a phonon-mediated interaction on a ladder. By applying the Abelian bosonization and two types of spin-chirality duality, we derive a comprehensive ground-state phase diagram that includes previously unexplored cases of a ferromagnetic rung exchange $J_\perp<0$ or a negative CCI $K_{\rm ch}<0$. The phase diagram consists of the rung singlet (RS) phase, the Haldane phase, and three non-magnetic ordered phases. Moreover, the RS and Haldane phases consist of several regions with different dominant correlations in terms of spin, dimer, or chirality. We perform numerical simulations to confirm the predicted phase structure and critical properties.

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We study the ground-state phase diagram of a spin- $\frac{1}{2}$ XXZ model with a chirality-chirality interaction (CCI) on a two-leg ladder. This model offers a minimal setup to study an interplay between spin and chirality degrees of freedom. The spin-chirality duality transformation allows us to relate the regimes of weak and strong CCIs. By applying the Abelian bosonization and the duality, we obtain a rich phase diagram that contains distinct gapped featureless and ordered phases. In particular, N\'eel and vector chiral orders appear for easy-axis anisotropy, while two distinct symmetry-protected topological (SPT) phases appear for easy-plane anisotropy. The two SPT phases can be viewed as twisted variants of the Haldane phase. We also present an effective description in terms of (spinor) hard-core bosons, which reveals critical behavior on the self-dual line in the easy-axis and easy-plane regimes. We perform numerical simulations to confirm the predicted phase structure and critical properties. We further demonstrate that the two SPT phases and a trivial phase are distinguished by topological indices in the presence of certain symmetries. A similar phase structure is expected in a spin- $\frac{1}{2}$ XXZ ladder with four-spin ring exchange.We study the ground-state phase diagram of a spin-$\frac{1}{2}$ XXZ model with a chirality-chirality interaction (CCI) on a two-leg ladder. This model offers a minimal setup to study an interplay between spin and chirality degrees of freedom. The spin-chirality duality transformation allows us to relate the regimes of weak and strong CCIs. By applying the Abelian bosonization and the duality, we obtain a rich phase diagram that contains distinct gapped featureless and ordered phases. In particular, N\'eel and vector chiral orders appear for easy-axis anisotropy, while two distinct symmetry-protected topological (SPT) phases appear for easy-plane anisotropy. The two SPT phases can be viewed as twisted variants of the Haldane phase. We also present an effective description in terms of (spinor) hard-core bosons, which reveals critical behavior on the self-dual line in the easy-axis and easy-plane regimes. We perform numerical simulations to confirm the predicted phase structure and critical properties. We further demonstrate that the two SPT phases and a trivial phase are distinguished by topological indices in the presence of certain symmetries. A similar phase structure is expected in a spin-$\frac{1}{2}$ XXZ ladder with four-spin ring exchange.

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A spin- $\frac{1}{2}$ two-leg ladder with four-spin ring exchange is studied by quantized Berry phases, used as local-order parameters. Reflecting local objects, nontrivial $(\ensuremath{\pi})$ Berry phase is founded on a rung for the rung-singlet phase and on a plaquette for the vector-chiral phase. Since the quantized Berry phase is topologically invariant for gapped systems with the time-reversal symmetry, topologically identical models can be obtained by the adiabatic modification. The rung-singlet phase is adiabatically connected to a decoupled rung-singlet model and the vector-chiral phase is connected to a decoupled vector-chiral model. Decoupled models reveal that the local objects are a local singlet and a plaquette singlet, respectively.A spin-$\frac{1}{2}$ two-leg ladder with four-spin ring exchange is studied by quantized Berry phases, used as local-order parameters. Reflecting local objects, nontrivial $(\ensuremath{\pi})$ Berry phase is founded on a rung for the rung-singlet phase and on a plaquette for the vector-chiral phase. Since the quantized Berry phase is topologically invariant for gapped systems with the time-reversal symmetry, topologically identical models can be obtained by the adiabatic modification. The rung-singlet phase is adiabatically connected to a decoupled rung-singlet model and the vector-chiral phase is connected to a decoupled vector-chiral model. Decoupled models reveal that the local objects are a local singlet and a plaquette singlet, respectively.

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Phases of the generalized two-leg spin ladder: A view from the SU(4) symmetry

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The zero-temperature phases of a generalized two-leg spin ladder with four-spin exchanges are discussed by means of a low-energy field theory approach starting from an SU(4) quantum critical point. The latter fixed point is shown to be a rich multicritical point that unifies different competing dimerized orders and a scalar chirality phase that breaks spontaneously the time-reversal symmetry. The quantum phase transition between these phases is dominated by spin-singlet fluctuations and belongs to the Luttinger universality class due to the existence of a $\mathrm{U}(1)$ self-duality symmetry.The zero-temperature phases of a generalized two-leg spin ladder with four-spin exchanges are discussed by means of a low-energy field theory approach starting from an SU(4) quantum critical point. The latter fixed point is shown to be a rich multicritical point that unifies different competing dimerized orders and a scalar chirality phase that breaks spontaneously the time-reversal symmetry. The quantum phase transition between these phases is dominated by spin-singlet fluctuations and belongs to the Luttinger universality class due to the existence of a $\mathrm{U}(1)$ self-duality symmetry.

arXiv:cond-mat/0405275Physical Review BJan 27, 200523 citations

J_\perp<0

or a negative CCI

K_{\rm ch}<0

. The phase diagram consists of the rung singlet (RS) phase, the Haldane phase, and three non-magnetic ordered phases. Moreover, the RS and Haldane phases consist of several regions with different dominant correlations in terms of spin, dimer, or chirality. We perform numerical simulations to confirm the predicted phase structure and critical properties.

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 study the ground-state phase diagram of a spin-

\frac{1}{2}

XXZ model with a chirality-chirality interaction (CCI) on a two-leg ladder. This model offers a minimal setup to study an interplay between spin and chirality degrees of freedom. The spin-chirality duality transformation allows us to relate the regimes of weak and strong CCIs. By applying the Abelian bosonization and the duality, we obtain a rich phase diagram that contains distinct gapped featureless and ordered phases. In particular, N\'eel and vector chiral orders appear for easy-axis anisotropy, while two distinct symmetry-protected topological (SPT) phases appear for easy-plane anisotropy. The two SPT phases can be viewed as twisted variants of the Haldane phase. We also present an effective description in terms of (spinor) hard-core bosons, which reveals critical behavior on the self-dual line in the easy-axis and easy-plane regimes. We perform numerical simulations to confirm the predicted phase structure and critical properties. We further demonstrate that the two SPT phases and a trivial phase are distinguished by topological indices in the presence of certain symmetries. A similar phase structure is expected in a spin-

\frac{1}{2}

XXZ ladder with four-spin ring exchange.

A spin-

\frac{1}{2}

two-leg ladder with four-spin ring exchange is studied by quantized Berry phases, used as local-order parameters. Reflecting local objects, nontrivial $(\ensuremath{\pi})$ Berry phase is founded on a rung for the rung-singlet phase and on a plaquette for the vector-chiral phase. Since the quantized Berry phase is topologically invariant for gapped systems with the time-reversal symmetry, topologically identical models can be obtained by the adiabatic modification. The rung-singlet phase is adiabatically connected to a decoupled rung-singlet model and the vector-chiral phase is connected to a decoupled vector-chiral model. Decoupled models reveal that the local objects are a local singlet and a plaquette singlet, respectively.

\mathrm{U}(1)

self-duality symmetry.