arXiv:cond-mat/0612271 · Physical Review B

Quantum phase transitions in trimerized zigzag spin ladders

H. D. Rosales, D. C. Cabra, Marcelo D. Grynberg, G. L. Rossini, T. Vekua

Published May 31, 2007• 3 citations

Abstract

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.

DOI: 10.1103/physrevb.75.174446

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Magnetization Plateau in the Spin S=1/2 Two-Leg Ladder with Trimerized Modulation of the Rung Exchange

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arXiv:cond-mat/0612271 · Physical Review B

Quantum phase transitions in trimerized zigzag spin ladders

H. D. Rosales, D. C. Cabra, Marcelo D. Grynberg, G. L. Rossini, T. Vekua

Published May 31, 2007• 3 citations

arXiv HTML PDF

Abstract

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.

DOI: 10.1103/physrevb.75.174446

Related papers

Magnetization Plateau in the Spin S=1/2 Two-Leg Ladder with Trimerized Modulation of the Rung Exchange

Niko Avalishvili, G. I. Japaridze, David Nozadze +1 more

The ground-state magnetic phase diagram of a two-leg spin ladder with trimerized modulated rung exchange is studied using the continuum-limit bosonization approach. In the limit where the rung exchange is dominant, the model is mapped onto the effective quantum sine-Gordon model with topological term. Six quantum phase transitions at different critical magnetic fields are identified. We have shown that the magnetization curve of the system exhibits two plateaus at magnetization equal to the 1/3 and 2/3 of the saturation value. The width of the plateaus is proportional to the excitation gap at given magnetization and scales as   , where  is the amplitude of rung exchange modulation and the criticalThe ground-state magnetic phase diagram of a two-leg spin ladder with trimerized modulated rung exchange is studied using the continuum-limit bosonization approach. In the limit where the rung exchange is dominant, the model is mapped onto the effective quantum sine-Gordon model with topological term. Six quantum phase transitions at different critical magnetic fields are identified. We have shown that the magnetization curve of the system exhibits two plateaus at magnetization equal to the 1/3 and 2/3 of the saturation value. The width of the plateaus is proportional to the excitation gap at given magnetization and scales as   , where  is the amplitude of rung exchange modulation and the critical

Jan 1, 20120 citations

Frustration effects on the magnetization plateau physics in a trimerized quantum spin-1/2 chain

L. M. Ramos, M. Schmidt, Fábio M. Zimmer

We investigate frustration-induced instabilities in a trimerized quantum spin chain motivated by recent experimental findings for the compound Na $_2$ Cu $_3$ Ge $_4$ O $_{12}$ . Employing a cluster mean-field approach combined with Lanczos exact diagonalization, we analyze the ground-state and quantum-information properties of a Heisenberg model with competing interactions in a magnetic field. In the weakly frustrated regime, the system exhibits a robust $1/3$ magnetization plateau associated with a collective ferrimagnetic-like trimer state. Increasing the next-nearest-neighbor intratrimer coupling drives a pronounced reorganization of spin correlations, leading to a crossover toward a doublon-like correlation regime and providing a static ground-state picture consistent with the composite excitations observed dynamically in trimerized chains. The resulting low-energy behavior can be interpreted in terms of weakly interacting emergent spins, offering a microscopic explanation for the extended stability of the magnetization plateau. Furthermore, through finite-size scaling analyses of the energy gap, von Neumann entanglement entropy, and fidelity susceptibility, we characterize the zero-field criticality of the model. Ultimately, our results suggest that frustration gives rise to qualitatively distinct quantum states and provide a microscopic framework for understanding the emergence of fractionalized excitations in trimerized quantum spin systems.We investigate frustration-induced instabilities in a trimerized quantum spin chain motivated by recent experimental findings for the compound Na$_2$Cu$_3$Ge$_4$O$_{12}$. Employing a cluster mean-field approach combined with Lanczos exact diagonalization, we analyze the ground-state and quantum-information properties of a Heisenberg model with competing interactions in a magnetic field. In the weakly frustrated regime, the system exhibits a robust $1/3$ magnetization plateau associated with a collective ferrimagnetic-like trimer state. Increasing the next-nearest-neighbor intratrimer coupling drives a pronounced reorganization of spin correlations, leading to a crossover toward a doublon-like correlation regime and providing a static ground-state picture consistent with the composite excitations observed dynamically in trimerized chains. The resulting low-energy behavior can be interpreted in terms of weakly interacting emergent spins, offering a microscopic explanation for the extended stability of the magnetization plateau. Furthermore, through finite-size scaling analyses of the energy gap, von Neumann entanglement entropy, and fidelity susceptibility, we characterize the zero-field criticality of the model. Ultimately, our results suggest that frustration gives rise to qualitatively distinct quantum states and provide a microscopic framework for understanding the emergence of fractionalized excitations in trimerized quantum spin systems.

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Quantum phases of spin-1 system on 3/4 and 3/5 skewed ladders

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We study the quantum phase transitions of frustrated antiferromagnetic Heisenberg spin-1 systems on the 3/4 and 3/5 skewed two leg ladder geometries. These systems can be viewed as arising by periodically removing rung bonds from a zigzag ladder. We find that in large systems, the ground state (gs) of the 3/4 ladder switches from a singlet to a magnetic state for J1≥1.82; the gs spin corresponds to the ferromagnetic alignment of effective S=2 objects on each unit cell. The gs of antiferromagnetic exchange Heisenberg spin-1 system on a 3/5 skewed ladder is highly frustrated and has spiral spin arrangements. The amplitude of the spin density wave in the 3/5 ladder is significantly larger compared to that in the magnetic state of the 3/4 ladder. The gs of the system switches between singlet state and low spin magnetic states multiple times on tuning J1 in a finite size system. The switching pattern is nonmonotonic as a function of J1 and depends on the system size. It appears to be the consequence of a higher J1 favoring a higher spin magnetic state and the finite system favoring a standing spin wave. For some specific parameter values, the magnetic gs in the 3/5 system is doubly degenerate in two different mirror symmetry subspaces. This degeneracy leads to spontaneous spin-parity and mirror symmetry breaking, giving rise to spin current in the gs of the system.We study the quantum phase transitions of frustrated antiferromagnetic Heisenberg spin-1 systems on the 3/4 and 3/5 skewed two leg ladder geometries. These systems can be viewed as arising by periodically removing rung bonds from a zigzag ladder. We find that in large systems, the ground state (gs) of the 3/4 ladder switches from a singlet to a magnetic state for J1≥1.82; the gs spin corresponds to the ferromagnetic alignment of effective S=2 objects on each unit cell. The gs of antiferromagnetic exchange Heisenberg spin-1 system on a 3/5 skewed ladder is highly frustrated and has spiral spin arrangements. The amplitude of the spin density wave in the 3/5 ladder is significantly larger compared to that in the magnetic state of the 3/4 ladder. The gs of the system switches between singlet state and low spin magnetic states multiple times on tuning J1 in a finite size system. The switching pattern is nonmonotonic as a function of J1 and depends on the system size. It appears to be the consequence of a higher J1 favoring a higher spin magnetic state and the finite system favoring a standing spin wave. For some specific parameter values, the magnetic gs in the 3/5 system is doubly degenerate in two different mirror symmetry subspaces. This degeneracy leads to spontaneous spin-parity and mirror symmetry breaking, giving rise to spin current in the gs of the system.

arXiv:2103.00150Journal of Applied PhysicsJun 8, 20215 citations

Magnetization Plateau of theS= 1/2 Frustrated Heisenberg Chain with Period 3 Parity Invariant Exchange Modulation

Kazuo Hida, Ian K. Affleck

The magnetization plateau of the S = 1/2 frustrated Heisenberg chain with period 3 parity invariant exchange modulation is investigated by the bosonization and numerical exact diagonalization method. The ground state phase diagram at 1/3 of the saturated magnetization is obtained. Among three degenerate ↑↑↓-type plateau states in the uniform chain, two of them (↓↑↑↓↑↑⋅⋅⋅ and ↑↓↑↑↓↑⋅⋅⋅) turned out to be robust against the period 3 exchange modulation which favors the phase up to a critical value of the modulation amplitude ( = singlet dimer) resulting in the Z2 symmetry broken phase. Another ↑↑↓-type state with ↑↑↓↑↑↓⋅⋅⋅ configuration is stabilized for period 3 modulation with opposite sign. The transition between the -phase and Z2-broken phase is the Ising transition and that between the ↑↑↓↑↑↓⋅⋅⋅ -phase and Z2 broken phase is the first order transition. The spin configuration in each phase is numerically verified by applying the local symmetry breaking field.The magnetization plateau of the S = 1/2 frustrated Heisenberg chain with period 3 parity invariant exchange modulation is investigated by the bosonization and numerical exact diagonalization method. The ground state phase diagram at 1/3 of the saturated magnetization is obtained. Among three degenerate ↑↑↓-type plateau states in the uniform chain, two of them (↓↑↑↓↑↑⋅⋅⋅ and ↑↓↑↑↓↑⋅⋅⋅) turned out to be robust against the period 3 exchange modulation which favors the phase up to a critical value of the modulation amplitude ( = singlet dimer) resulting in the Z2 symmetry broken phase. Another ↑↑↓-type state with ↑↑↓↑↑↓⋅⋅⋅ configuration is stabilized for period 3 modulation with opposite sign. The transition between the -phase and Z2-broken phase is the Ising transition and that between the ↑↑↓↑↑↓⋅⋅⋅ -phase and Z2 broken phase is the first order transition. The spin configuration in each phase is numerically verified by applying the local symmetry breaking field.

Progress of Theoretical Physics SupplementJan 1, 20050 citations

Ground state and excitation of an asymmetric spin ladder model

Shu Chen, H. Büttner, Johannes Voit

We perform a systematic investigation on an asymmetric zigzag spin ladder with interleg exchange ${J}_{1}$ and different exchange integrals ${J}_{2}\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta}$ on both legs. In the weak frustration limit, the spin model can be mapped to a revised double frequency sine-Gordon model by using bosonization. Renormalization-group analysis shows that the Heisenberg critical point flows to an intermediate-coupling fixed point with gapless excitations and a vanishing spin velocity. When the frustration is large, a spin gap opens and a dimer ground state is realized. Fixing ${J}_{2}{=J}_{1}/2,$ we find, as a function of $\ensuremath{\delta},$ a continuous manifold of Hamiltonians with dimer product ground states, interpolating between the Majumdar-Ghosh and sawtooth spin-chain model. While the ground state is independent of the alternating next-nearest-neighbor exchange $\ensuremath{\delta},$ the gap size of excitations is found to decrease with increasing $\ensuremath{\delta}.$ We also extend our study to a two-dimensional double layer model with an exactly known ground state.We perform a systematic investigation on an asymmetric zigzag spin ladder with interleg exchange ${J}_{1}$ and different exchange integrals ${J}_{2}\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta}$ on both legs. In the weak frustration limit, the spin model can be mapped to a revised double frequency sine-Gordon model by using bosonization. Renormalization-group analysis shows that the Heisenberg critical point flows to an intermediate-coupling fixed point with gapless excitations and a vanishing spin velocity. When the frustration is large, a spin gap opens and a dimer ground state is realized. Fixing ${J}_{2}{=J}_{1}/2,$ we find, as a function of $\ensuremath{\delta},$ a continuous manifold of Hamiltonians with dimer product ground states, interpolating between the Majumdar-Ghosh and sawtooth spin-chain model. While the ground state is independent of the alternating next-nearest-neighbor exchange $\ensuremath{\delta},$ the gap size of excitations is found to decrease with increasing $\ensuremath{\delta}.$ We also extend our study to a two-dimensional double layer model with an exactly known ground state.

arXiv:cond-mat/0201004Physical review. B, Condensed matterFeb 10, 200333 citations

Frustration-induced plateaus in S≥12 Heisenberg spin ladders

Frédéric Michaud, Tommaso Coletta, Salvatore R. Manmana +2 more

We study the $T=0$ magnetization of frustrated two-leg spin ladders with arbitrary value of the spin $S$ . In the strong-rung limit, we use degenerate perturbation theory to prove that frustration leads to magnetization plateaus at fractional values of the magnetization for all spins $S$ and to determine the critical ratios of parallel to diagonal inter-rung couplings for the appearance of these plateaus. These ratios depend both on the plateau and on the spin. To confirm these results and to investigate the properties of these ladders away from the strong-coupling limit, we have performed extensive density-matrix renormalization-group calculations for $S\ensuremath{\le}2$. For large enough inter-rung couplings, all plateaus simply disappear, leading to a magnetization curve typical of integer-spin chains in a magnetic field. The intermediate region turns out to be surprisingly rich however, with, upon increasing the inter-rung couplings, the development of magnetization jumps and, in some cases, the appearance of one or more phase transitions inside a given plateau.We study the $T=0$ magnetization of frustrated two-leg spin ladders with arbitrary value of the spin $S$. In the strong-rung limit, we use degenerate perturbation theory to prove that frustration leads to magnetization plateaus at fractional values of the magnetization for all spins $S$ and to determine the critical ratios of parallel to diagonal inter-rung couplings for the appearance of these plateaus. These ratios depend both on the plateau and on the spin. To confirm these results and to investigate the properties of these ladders away from the strong-coupling limit, we have performed extensive density-matrix renormalization-group calculations for $S\ensuremath{\le}2$. For large enough inter-rung couplings, all plateaus simply disappear, leading to a magnetization curve typical of integer-spin chains in a magnetic field. The intermediate region turns out to be surprisingly rich however, with, upon increasing the inter-rung couplings, the development of magnetization jumps and, in some cases, the appearance of one or more phase transitions inside a given plateau.

arXiv:0907.1461Physical Review BJan 8, 201027 citations

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

We investigate frustration-induced instabilities in a trimerized quantum spin chain motivated by recent experimental findings for the compound Na

_2

_3

_4

_{12}

. Employing a cluster mean-field approach combined with Lanczos exact diagonalization, we analyze the ground-state and quantum-information properties of a Heisenberg model with competing interactions in a magnetic field. In the weakly frustrated regime, the system exhibits a robust

1/3

magnetization plateau associated with a collective ferrimagnetic-like trimer state. Increasing the next-nearest-neighbor intratrimer coupling drives a pronounced reorganization of spin correlations, leading to a crossover toward a doublon-like correlation regime and providing a static ground-state picture consistent with the composite excitations observed dynamically in trimerized chains. The resulting low-energy behavior can be interpreted in terms of weakly interacting emergent spins, offering a microscopic explanation for the extended stability of the magnetization plateau. Furthermore, through finite-size scaling analyses of the energy gap, von Neumann entanglement entropy, and fidelity susceptibility, we characterize the zero-field criticality of the model. Ultimately, our results suggest that frustration gives rise to qualitatively distinct quantum states and provide a microscopic framework for understanding the emergence of fractionalized excitations in trimerized quantum spin systems.

We perform a systematic investigation on an asymmetric zigzag spin ladder with interleg exchange

{J}_{1}

and different exchange integrals ${J}_{2}\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta}$ on both legs. In the weak frustration limit, the spin model can be mapped to a revised double frequency sine-Gordon model by using bosonization. Renormalization-group analysis shows that the Heisenberg critical point flows to an intermediate-coupling fixed point with gapless excitations and a vanishing spin velocity. When the frustration is large, a spin gap opens and a dimer ground state is realized. Fixing

{J}_{2}{=J}_{1}/2,

we find, as a function of $\ensuremath{\delta},$ a continuous manifold of Hamiltonians with dimer product ground states, interpolating between the Majumdar-Ghosh and sawtooth spin-chain model. While the ground state is independent of the alternating next-nearest-neighbor exchange $\ensuremath{\delta},$ the gap size of excitations is found to decrease with increasing $\ensuremath{\delta}.$ We also extend our study to a two-dimensional double layer model with an exactly known ground state.

We study the

T=0

magnetization of frustrated two-leg spin ladders with arbitrary value of the spin

S

. In the strong-rung limit, we use degenerate perturbation theory to prove that frustration leads to magnetization plateaus at fractional values of the magnetization for all spins

S

and to determine the critical ratios of parallel to diagonal inter-rung couplings for the appearance of these plateaus. These ratios depend both on the plateau and on the spin. To confirm these results and to investigate the properties of these ladders away from the strong-coupling limit, we have performed extensive density-matrix renormalization-group calculations for $S\ensuremath{\le}2$. For large enough inter-rung couplings, all plateaus simply disappear, leading to a magnetization curve typical of integer-spin chains in a magnetic field. The intermediate region turns out to be surprisingly rich however, with, upon increasing the inter-rung couplings, the development of magnetization jumps and, in some cases, the appearance of one or more phase transitions inside a given plateau.