Exploring quantum phases of the Zig-Zag chain

MAGNETIC PROPERTIES OF THE TWO-LEG ZIG-ZAG LADDER IN QUANTUM SPIN SYSTEM NH 4 CuCl 3 . Numerical analysis of the two-leg zig-zag ladder as a single chain with next-nearest neighbour interactions has been formulated by Cabra (1999) with the following Hamiltonian: Other formulation for two leg zig-zag ladder with dimmerized chains and coupling between the chains is as follow : From these formulations, we study the closing of the gap at zero magnetization by means of the fine—tuning mechanism and disappreance of the 1/2 plateau (gap) at ﬁnite by alternating dimerization of the chains along the rungs. We also described NH 4 CuCl 3 under high magnetic ﬁelds in a two-leg system.MAGNETIC PROPERTIES OF THE TWO-LEG ZIG-ZAG LADDER IN QUANTUM SPIN SYSTEM NH 4 CuCl 3 . Numerical analysis of the two-leg zig-zag ladder as a single chain with next-nearest neighbour interactions has been formulated by Cabra (1999) with the following Hamiltonian: Other formulation for two leg zig-zag ladder with dimmerized chains and coupling between the chains is as follow : From these formulations, we study the closing of the gap at zero magnetization by means of the fine—tuning mechanism and disappreance of the 1/2 plateau (gap) at ﬁnite by alternating dimerization of the chains along the rungs. We also described NH 4 CuCl 3 under high magnetic ﬁelds in a two-leg system.

Jan 1, 20020 citations

Quantum phases and connections

Jan Sładkowski

International Journal of Theoretical PhysicsJun 1, 19931 citation

Decoupling of the S=1/2 antiferromagnetic zig-zag ladder with anisotropy

Vitor Rocha Vieira, Nathalie Guihéry, J. P. Rodriguez +1 more

The spin-1/2 antiferromagnetic zig-zag ladder is studied by exact diagonalization of small systems in the regime of weak interchain coupling. A gapless phase with quasi-long-range spiral correlations has been predicted to occur in this regime if easy-plane $(\mathrm{XY})$ anisotropy is present. We find in general that the finite zig-zag ladder shows three phases: a gapless collinear phase, a dimer phase, and a spiral phase. We study the level crossings of the spectrum, the dimer correlation function, the structure factor, and the spin stiffness within these phases, as well as at the transition points. As the interchain coupling decreases we observe a transition in the anisotropic $\mathrm{XY}$ case from a phase with a gap to a gapless phase that is best described by two decoupled antiferromagnetic chains. The isotropic and the anisotropic $\mathrm{XY}$ cases are found to be qualitatively the same, however, in the regime of weak interchain coupling for the small systems studied here. We attribute this to a finite-size effect in the isotropic zig-zag case that results from exponentially diverging antiferromagnetic correlations in the weak-coupling limit.The spin-1/2 antiferromagnetic zig-zag ladder is studied by exact diagonalization of small systems in the regime of weak interchain coupling. A gapless phase with quasi-long-range spiral correlations has been predicted to occur in this regime if easy-plane $(\mathrm{XY})$ anisotropy is present. We find in general that the finite zig-zag ladder shows three phases: a gapless collinear phase, a dimer phase, and a spiral phase. We study the level crossings of the spectrum, the dimer correlation function, the structure factor, and the spin stiffness within these phases, as well as at the transition points. As the interchain coupling decreases we observe a transition in the anisotropic $\mathrm{XY}$ case from a phase with a gap to a gapless phase that is best described by two decoupled antiferromagnetic chains. The isotropic and the anisotropic $\mathrm{XY}$ cases are found to be qualitatively the same, however, in the regime of weak interchain coupling for the small systems studied here. We attribute this to a finite-size effect in the isotropic zig-zag case that results from exponentially diverging antiferromagnetic correlations in the weak-coupling limit.

arXiv:cond-mat/0104090Physical review. B, Condensed matterMay 22, 20017 citations

Quantum phases

Richard Montgomery

Mathematical surveys and monographsAug 8, 20060 citations

Magnetic Properties of Zig-Zag Ladders ∗

D. C. Cabra, A. Honecker, Pierre Pujol

We analyze the phase diagram of a system of spin-1/2 Heisenberg antiferromagnetic chains interacting through a zig-zag coupling, also called zig-zag ladders. Using bosonization techniques we study how a spin-gap or more generally plateaux in magnetization curves arise in different situations. While for coupled XXZ chains, one has to deal with a recently discovered chiral perturbation, the coupling term which is present for normal ladders is restored by an external magnetic field, dimerization or the presence of charge carriers. We then proceed with a numerical investigation of the phase diagram of two coupled Heisenberg chains in the presence of a magnetic field. Unusual behaviour is found for ferromagnetic coupled antiferromagnetic chains. Finally, for three (and more) legs one can choose different inequivalent types of coupling between the chains. We find that the three-leg ladder can exhibit a spin-gap and/or non-trivial plateaux in the magnetization curve whose appearance strongly depends on the choice of coupling.We analyze the phase diagram of a system of spin-1/2 Heisenberg antiferromagnetic chains interacting through a zig-zag coupling, also called zig-zag ladders. Using bosonization techniques we study how a spin-gap or more generally plateaux in magnetization curves arise in different situations. While for coupled XXZ chains, one has to deal with a recently discovered chiral perturbation, the coupling term which is present for normal ladders is restored by an external magnetic field, dimerization or the presence of charge carriers. We then proceed with a numerical investigation of the phase diagram of two coupled Heisenberg chains in the presence of a magnetic field. Unusual behaviour is found for ferromagnetic coupled antiferromagnetic chains. Finally, for three (and more) legs one can choose different inequivalent types of coupling between the chains. We find that the three-leg ladder can exhibit a spin-gap and/or non-trivial plateaux in the magnetization curve whose appearance strongly depends on the choice of coupling.

Jan 1, 199951 citations

(\mathrm{XY})

anisotropy is present. We find in general that the finite zig-zag ladder shows three phases: a gapless collinear phase, a dimer phase, and a spiral phase. We study the level crossings of the spectrum, the dimer correlation function, the structure factor, and the spin stiffness within these phases, as well as at the transition points. As the interchain coupling decreases we observe a transition in the anisotropic

\mathrm{XY}

case from a phase with a gap to a gapless phase that is best described by two decoupled antiferromagnetic chains. The isotropic and the anisotropic

\mathrm{XY}

cases are found to be qualitatively the same, however, in the regime of weak interchain coupling for the small systems studied here. We attribute this to a finite-size effect in the isotropic zig-zag case that results from exponentially diverging antiferromagnetic correlations in the weak-coupling limit.