© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:cond-mat/9904371 · Journal of Physics Condensed Matter

Effective theory of magnetization plateaus in a three-leg ladder with periodic boundary conditions

R. Citro, E. Orignac, Natan Andrei, Chigak Itoi, S Qin

Published Mar 15, 2000• 23 citations

Abstract

We show that the low-energy physics of the three-leg-ladder model in the presence of a critical magnetic field can be described by a broken SU(3) spin chain for a periodic rung model and a broken SU(2) spin chain for an open rung model. Using the Lieb-Schultz-Mattis theorem we characterize the possible magnetization plateaus and study the critical behaviour in the region of transition between the plateaus S z = 1/2 and S z = 3/2 by means of renormalization group calculations performed on the bosonized effective continuum field theory. We show that in certain regions of the parameter space of the effective theory the system remains gapless, and we compute the spin-spin correlation functions for these regions. We also discuss the possibility of a plateau at S z = 1, and show that although there exists in the continuum theory a term that might cause the appearance of a plateau there, such a term is unlikely to be relevant. This conjecture is proved by density-matrix renormalization group (DMRG) techniques. The modifications of the three-leg-ladder Hamiltonian that show plateaus at S z = 1, 5/6, 7/6 are discussed. We show the S z = 1 plateau in the XXZ -type modification by means of the DMRG technique. We find non-magnetic gapless excitation on this plateau in the periodic rung case.

DOI: 10.1088/0953-8984/12/13/315

Related papers

Magnetization properties of some quantum spin ladders

Kunj Tandon, Siddhartha Lal, Swapan Kumar Pati +2 more

The experimental realization of various spin ladder systems has prompted their detailed theoretical investigations. Here we study the evolution of ground-state magnetization with an external magnetic field for two different antiferromagnetic systems: a three-legged spin-$1/2$ ladder, and a two-legged spin-$1/2$ ladder with an additional diagonal interaction. The finite system density-matrix renormalization-group method is employed for numerical studies of the three-chain system, and an effective low-energy Hamiltonian is used in the limit of strong interchain coupling to study the two- and three-chain systems. The three-chain system has a magnetization plateau at one-third of the saturation magnetization. The two-chain system has a plateau at zero magnetization due to a gap above the singlet ground state. It also has a plateau at half of the saturation magnetization for a certain range of values of the couplings. We study the regions of transitions between plateaus numerically and analytically, and find that they are described, at first order in a strong-coupling expansion, by an $\mathrm{XXZ}$ spin-$1/2$ chain in a magnetic field; the second-order terms give corrections to the $\mathrm{XXZ}$ model. We also study numerically some low-temperature properties of the three-chain system, such as the magnetization, magnetic susceptibility and specific heat.

arXiv:cond-mat/9806111•Physical review. B, Condensed matter•Jan 1, 1999•63 citations

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 critical

•Jan 1, 2012•0 citations

Low-energy properties and magnetization plateaus in a two-leg mixed spin ladder

Jizhong Lou, Changfeng Chen, Shaojin Qin

Using the density-matrix renormalization-group technique we investigate the low-energy properties and the magnetization-plateau behavior in a two-leg mixed spin ladder consisting of a spin-1/2 chain coupled with a spin-1 chain. The calculated results show that the system is in the same universality class as the spin-3/2 chain when the interchain coupling is strongly ferromagnetic, but the similarity between the two systems is less clear under other coupling conditions. We have identified two types of magnetization-plateau phases. The calculation of the magnetization distribution on the spin-1/2 and the spin-1 chains on the ladder shows that one plateau phase is related to the partially magnetized valence-bond-solid state, and the other plateau state contains strongly coupled $S=1$ and $s=1/2$ spins on the rung.

arXiv:cond-mat/0109014•Physical review. B, Condensed matter•Aug 29, 2001•10 citations

Magnetization plateaus by reconstructed quasispinons in a frustrated two-leg spin ladder under a magnetic field

Takanori Sugimoto, Michiyasu Mori, Takami Tohyama +1 more

The quantum phase transitions induced by a magnetic field are theoretically studied in a frustrated two-leg spin ladder. Using the density-matrix renormalization-group method, we find some magnetic phase transitions and plateaus in two different cases of strong and weak rung couplings. With the strong rung coupling, the three magnetization plateaus are found at 1/3, 1/2, and 2/3 due to the frustration. Those can be understood in terms of a quasispinon reconstructed from the singlet and the triplets of spins on a rung. The plateau at 1/2 corresponds to the valence bond solid of the quasispinons, while the plateaus at 1/3 and 2/3 can be associated with the array of quasispinons such as the soliton lattice. This is different from the usual Bose-Einstein-condensation picture of triplons. Our results will be useful in understanding magnetization curves in ${\mathrm{BiCu}}_{2}{\mathrm{PO}}_{6}$.

arXiv:1505.01610•Physical Review B•Sep 9, 2015•16 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.

arXiv:0907.1461•Physical Review B•Jan 8, 2010•27 citations

The energy spectrum and magnetization profile of the decorated spin ladder systems

Vladyslav O. Cheranovskii, E. V. Ezerskaya, S. Ye. Kononenko

The peculiarities of the energy spectrum of the decorated mixed spin two-leg ladder system having three spin unit cells have been studied by the perturbation theory in the limit of dominant spin coupling in ladder rungs. It is shown, that despite the singlet ground state, this spin ladder may have an intermediate plateau in a low-temperature magnetization profile. The existence of a similar plateau was shown also in the case of some intermediate values of coupling parameters by means of exact diagonalization study of small ladder clusters and by the density-matrix renormalization group calculations. We also found that the Ising type of interactions in ladder rungs may lead to the disappearance of the above intermediate magnetization plateau for the corresponding isotropic spin ladder.

Low Temperature Physics•Feb 1, 2024•1 citation

We show that the low-energy physics of the three-leg-ladder model in the presence of a critical magnetic field can be described by a broken SU(3) spin chain for a periodic rung model and a broken SU(2) spin chain for an open rung model. Using the Lieb-Schultz-Mattis theorem we characterize the possible magnetization plateaus and study the critical behaviour in the region of transition between the plateaus S z = 1/2 and S z = 3/2 by means of renormalization group calculations performed on the bosonized effective continuum field theory. We show that in certain regions of the parameter space of the effective theory the system remains gapless, and we compute the spin-spin correlation functions for these regions. We also discuss the possibility of a plateau at S z = 1, and show that although there exists in the continuum theory a term that might cause the appearance of a plateau there, such a term is unlikely to be relevant. This conjecture is proved by density-matrix renormalization group (DMRG) techniques. The modifications of the three-leg-ladder Hamiltonian that show plateaus at S z = 1, 5/6, 7/6 are discussed. We show the S z = 1 plateau in the XXZ -type modification by means of the DMRG technique. We find non-magnetic gapless excitation on this plateau in the periodic rung case.

The experimental realization of various spin ladder systems has prompted their detailed theoretical investigations. Here we study the evolution of ground-state magnetization with an external magnetic field for two different antiferromagnetic systems: a three-legged spin-

1/2

ladder, and a two-legged spin-

1/2

ladder with an additional diagonal interaction. The finite system density-matrix renormalization-group method is employed for numerical studies of the three-chain system, and an effective low-energy Hamiltonian is used in the limit of strong interchain coupling to study the two- and three-chain systems. The three-chain system has a magnetization plateau at one-third of the saturation magnetization. The two-chain system has a plateau at zero magnetization due to a gap above the singlet ground state. It also has a plateau at half of the saturation magnetization for a certain range of values of the couplings. We study the regions of transitions between plateaus numerically and analytically, and find that they are described, at first order in a strong-coupling expansion, by an

\mathrm{XXZ}

spin-

1/2

chain in a magnetic field; the second-order terms give corrections to the

\mathrm{XXZ}

model. We also study numerically some low-temperature properties of the three-chain system, such as the magnetization, magnetic susceptibility and specific heat.

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 critical

Using the density-matrix renormalization-group technique we investigate the low-energy properties and the magnetization-plateau behavior in a two-leg mixed spin ladder consisting of a spin-1/2 chain coupled with a spin-1 chain. The calculated results show that the system is in the same universality class as the spin-3/2 chain when the interchain coupling is strongly ferromagnetic, but the similarity between the two systems is less clear under other coupling conditions. We have identified two types of magnetization-plateau phases. The calculation of the magnetization distribution on the spin-1/2 and the spin-1 chains on the ladder shows that one plateau phase is related to the partially magnetized valence-bond-solid state, and the other plateau state contains strongly coupled

S=1

and

\mathrm{XXZ}

spins on the rung.

The quantum phase transitions induced by a magnetic field are theoretically studied in a frustrated two-leg spin ladder. Using the density-matrix renormalization-group method, we find some magnetic phase transitions and plateaus in two different cases of strong and weak rung couplings. With the strong rung coupling, the three magnetization plateaus are found at 1/3, 1/2, and 2/3 due to the frustration. Those can be understood in terms of a quasispinon reconstructed from the singlet and the triplets of spins on a rung. The plateau at 1/2 corresponds to the valence bond solid of the quasispinons, while the plateaus at 1/3 and 2/3 can be associated with the array of quasispinons such as the soliton lattice. This is different from the usual Bose-Einstein-condensation picture of triplons. Our results will be useful in understanding magnetization curves in

{\mathrm{BiCu}}_{2}{\mathrm{PO}}_{6}

.

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.

The peculiarities of the energy spectrum of the decorated mixed spin two-leg ladder system having three spin unit cells have been studied by the perturbation theory in the limit of dominant spin coupling in ladder rungs. It is shown, that despite the singlet ground state, this spin ladder may have an intermediate plateau in a low-temperature magnetization profile. The existence of a similar plateau was shown also in the case of some intermediate values of coupling parameters by means of exact diagonalization study of small ladder clusters and by the density-matrix renormalization group calculations. We also found that the Ising type of interactions in ladder rungs may lead to the disappearance of the above intermediate magnetization plateau for the corresponding isotropic spin ladder.