We study an isotropic Heisenberg spin- $\frac{1}{2}$ model on a trellis ladder which is composed of two ${J}_{1}\ensuremath{-}{J}_{2}$ zigzag ladders interacting through antiferromagnetic rung coupling ${J}_{3}$ . ${J}_{1}$ and ${J}_{2}$ are ferromagnetic zigzag spin interaction between two legs and antiferromagnetic interaction along each leg of a zigzag ladder. A quantum phase diagram of this model is constructed using the density matrix renormalization group method and linearized spin-wave analysis. In the small ${J}_{2}$ limit, a short-range striped collinear phase is found in the presence of ${J}_{3}$ , whereas, in the large ${J}_{2}/{J}_{3}$ limit, a noncollinear quasi-long-range phase is found. The system shows a short-range noncollinear state in the large ${J}_{3}$ limit. The short-range-order phase is the dominant feature of this phase diagram. We also show that the results obtained by DMRG and linearized spin-wave analysis show a similar phase boundary between the collinear striped and noncollinear short-range phases, and the collinear phase region shrinks with increasing ${J}_{3}$ . We apply this model to understand the magnetic properties of ${\mathrm{CaV}}_{2}{\mathrm{O}}_{5}$ and also fit the experimental data of susceptibility and magnetization. We note that ${J}_{3}$ is a dominant interaction in this material, whereas ${J}_{1}$ and ${J}_{2}$ are approximately half of ${J}_{3}$ . The variation of magnetic specific heat capacity as a function of temperature for various external magnetic fields is also predicted.We study an isotropic Heisenberg spin-$\frac{1}{2}$ model on a trellis ladder which is composed of two ${J}_{1}\ensuremath{-}{J}_{2}$ zigzag ladders interacting through antiferromagnetic rung coupling ${J}_{3}$. ${J}_{1}$ and ${J}_{2}$ are ferromagnetic zigzag spin interaction between two legs and antiferromagnetic interaction along each leg of a zigzag ladder. A quantum phase diagram of this model is constructed using the density matrix renormalization group method and linearized spin-wave analysis. In the small ${J}_{2}$ limit, a short-range striped collinear phase is found in the presence of ${J}_{3}$, whereas, in the large ${J}_{2}/{J}_{3}$ limit, a noncollinear quasi-long-range phase is found. The system shows a short-range noncollinear state in the large ${J}_{3}$ limit. The short-range-order phase is the dominant feature of this phase diagram. We also show that the results obtained by DMRG and linearized spin-wave analysis show a similar phase boundary between the collinear striped and noncollinear short-range phases, and the collinear phase region shrinks with increasing ${J}_{3}$. We apply this model to understand the magnetic properties of ${\mathrm{CaV}}_{2}{\mathrm{O}}_{5}$ and also fit the experimental data of susceptibility and magnetization. We note that ${J}_{3}$ is a dominant interaction in this material, whereas ${J}_{1}$ and ${J}_{2}$ are approximately half of ${J}_{3}$. The variation of magnetic specific heat capacity as a function of temperature for various external magnetic fields is also predicted.

arXiv:1907.04709Physical review. B./Physical review. BDec 10, 20198 citations

Quantum phase transitions in trimerized zigzag spin ladders

H. D. Rosales, D. C. Cabra, Marcelo D. Grynberg +2 more

We analyze the effects of a trimerized modulation in a quantum spin $S=\frac{1}{2}$ zigzag ladder at the magnetization plateau $M=1∕3$ . Such periodicity is argued to be stemmed from lattice deformations by phonons. The interplay between frustration and exchange modulation is well described by an effective triple sine-Gordon field theory close to the homogeneous ladder and by block-spin perturbation theory in the weakly coupled trimer regime. The characteristic triple degeneracy of the ground state for homogeneous ladders gives place to modulation driven quantum phase transitions, leading to a rich phase diagram including up-up-down, quantum plateau, and gapless plateau states.We analyze the effects of a trimerized modulation in a quantum spin $S=\frac{1}{2}$ zigzag ladder at the magnetization plateau $M=1∕3$. Such periodicity is argued to be stemmed from lattice deformations by phonons. The interplay between frustration and exchange modulation is well described by an effective triple sine-Gordon field theory close to the homogeneous ladder and by block-spin perturbation theory in the weakly coupled trimer regime. The characteristic triple degeneracy of the ground state for homogeneous ladders gives place to modulation driven quantum phase transitions, leading to a rich phase diagram including up-up-down, quantum plateau, and gapless plateau states.

arXiv:cond-mat/0612271Physical Review BMay 31, 20073 citations

Exact solution and magnetic properties of an anisotropic spin ladder

Zu-Jian Ying, I. Roditi, Angela Foerster +1 more

arXiv:cond-mat/0403520The European Physical Journal BSep 1, 20044 citations

Phase diagram of the Kondo model on the zigzag ladder

Matthias Peschke, Lena-Marie Woelk, Michael Potthoff

The effect of next-nearest-neighbor hopping ${t}_{2}$ on the ground-state phase diagram of the one-dimensional Kondo lattice is studied with density-matrix renormalization-group techniques and by comparing with the phase diagram of the classical-spin variant of the same model. For a finite ${t}_{2}$ , i.e., for a zigzag-ladder geometry, indirect antiferromagnetic interactions between the localized spins are geometrically frustrated. We demonstrate that ${t}_{2}$ at the same time triggers several magnetic phases which are absent in the model with nearest-neighbor hopping only. For strong $J$ , we find a transition from antiferromagnetic to incommensurate magnetic short-range order, which can be understood entirely in the classical-spin picture. For weaker $J$ , a spin-dimerized phase emerges, which spontaneously breaks the discrete translation symmetry. The phase is not accessible to perturbative means but is explained, on a qualitative level, by the classical-spin model as well. Spin dimerization alleviates magnetic frustration and is interpreted as a key to understand the emergence of quasi-long-range spiral magnetic order, which is found at weaker couplings. The phase diagram at weak $J$ , with gapless quasi-long-range order on top of the twofold degenerate spin-dimerized ground state, competing with a nondegenerate phase with gapped spin (and charge) excitations, is unconventional and eludes an effective low-energy spin-only theory.The effect of next-nearest-neighbor hopping ${t}_{2}$ on the ground-state phase diagram of the one-dimensional Kondo lattice is studied with density-matrix renormalization-group techniques and by comparing with the phase diagram of the classical-spin variant of the same model. For a finite ${t}_{2}$, i.e., for a zigzag-ladder geometry, indirect antiferromagnetic interactions between the localized spins are geometrically frustrated. We demonstrate that ${t}_{2}$ at the same time triggers several magnetic phases which are absent in the model with nearest-neighbor hopping only. For strong $J$, we find a transition from antiferromagnetic to incommensurate magnetic short-range order, which can be understood entirely in the classical-spin picture. For weaker $J$, a spin-dimerized phase emerges, which spontaneously breaks the discrete translation symmetry. The phase is not accessible to perturbative means but is explained, on a qualitative level, by the classical-spin model as well. Spin dimerization alleviates magnetic frustration and is interpreted as a key to understand the emergence of quasi-long-range spiral magnetic order, which is found at weaker couplings. The phase diagram at weak $J$, with gapless quasi-long-range order on top of the twofold degenerate spin-dimerized ground state, competing with a nondegenerate phase with gapped spin (and charge) excitations, is unconventional and eludes an effective low-energy spin-only theory.

arXiv:1901.01236Physical review. B./Physical review. BFeb 27, 20194 citations

Magnetic phase diagram of the spatially anisotropic spin-

1/2

zigzag ladder

We study an isotropic Heisenberg spin-

\frac{1}{2}

model on a trellis ladder which is composed of two ${J}_{1}\ensuremath{-}{J}_{2}$ zigzag ladders interacting through antiferromagnetic rung coupling

{J}_{3}

{J}_{1}

and

{J}_{2}

are ferromagnetic zigzag spin interaction between two legs and antiferromagnetic interaction along each leg of a zigzag ladder. A quantum phase diagram of this model is constructed using the density matrix renormalization group method and linearized spin-wave analysis. In the small

{J}_{2}

limit, a short-range striped collinear phase is found in the presence of

{J}_{3}

, whereas, in the large

{J}_{2}/{J}_{3}

limit, a noncollinear quasi-long-range phase is found. The system shows a short-range noncollinear state in the large

{J}_{3}

limit. The short-range-order phase is the dominant feature of this phase diagram. We also show that the results obtained by DMRG and linearized spin-wave analysis show a similar phase boundary between the collinear striped and noncollinear short-range phases, and the collinear phase region shrinks with increasing

{J}_{3}

. We apply this model to understand the magnetic properties of

{\mathrm{CaV}}_{2}{\mathrm{O}}_{5}

and also fit the experimental data of susceptibility and magnetization. We note that

{J}_{3}

is a dominant interaction in this material, whereas

{J}_{1}

and

{J}_{2}

are approximately half of

{J}_{3}

. The variation of magnetic specific heat capacity as a function of temperature for various external magnetic fields is also predicted.

We analyze the effects of a trimerized modulation in a quantum spin

S=\frac{1}{2}

zigzag ladder at the magnetization plateau

M=1∕3

. Such periodicity is argued to be stemmed from lattice deformations by phonons. The interplay between frustration and exchange modulation is well described by an effective triple sine-Gordon field theory close to the homogeneous ladder and by block-spin perturbation theory in the weakly coupled trimer regime. The characteristic triple degeneracy of the ground state for homogeneous ladders gives place to modulation driven quantum phase transitions, leading to a rich phase diagram including up-up-down, quantum plateau, and gapless plateau states.

The effect of next-nearest-neighbor hopping

{t}_{2}

on the ground-state phase diagram of the one-dimensional Kondo lattice is studied with density-matrix renormalization-group techniques and by comparing with the phase diagram of the classical-spin variant of the same model. For a finite

{t}_{2}

, i.e., for a zigzag-ladder geometry, indirect antiferromagnetic interactions between the localized spins are geometrically frustrated. We demonstrate that

{t}_{2}

at the same time triggers several magnetic phases which are absent in the model with nearest-neighbor hopping only. For strong

J

, we find a transition from antiferromagnetic to incommensurate magnetic short-range order, which can be understood entirely in the classical-spin picture. For weaker

J

, a spin-dimerized phase emerges, which spontaneously breaks the discrete translation symmetry. The phase is not accessible to perturbative means but is explained, on a qualitative level, by the classical-spin model as well. Spin dimerization alleviates magnetic frustration and is interpreted as a key to understand the emergence of quasi-long-range spiral magnetic order, which is found at weaker couplings. The phase diagram at weak

J

, with gapless quasi-long-range order on top of the twofold degenerate spin-dimerized ground state, competing with a nondegenerate phase with gapped spin (and charge) excitations, is unconventional and eludes an effective low-energy spin-only theory.