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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, S. Mahdavifar

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

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

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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
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We analyze the effects of a trimerized modulation in a quantum spin S=12S=\frac{1}{2}S=21​ zigzag ladder at the magnetization plateau M=1∕3M=1∕3M=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 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.
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A frustrated two‐legged spin‐1/2 ladder featuring alternating Ising and isotropic Heisenberg exchange interactions on the rungs is investigated, while Ising exchanges are present along the legs and diagonals. This model exhibits the following four ground‐state phases: (i) stripe rung ferromagnet (SRFM), (ii) anisotropic antiferromagnet, (iii) dimer, and (iv) stripe leg ferromagnet. In this work, different magnetization plateaus are analyzed by studying the spin density, quantum fidelity, and quantum concurrence in the presence of longitudinal and transverse magnetic fields. The exact diagonalization and transfer matrix methods are used to solve the model Hamiltonian. In the presence of a longitudinal field, the discrete magnetization plateaus appear at 0, 1/2, and 1 of the saturation value across all phases [(i)–(iv)]. Interestingly, in the presence of an externally applied transverse field, the SRFM phase [(i)] exhibits a continuous change in magnetization. The other three phases [(ii)–(iv)] show both discrete jump and continuous change in magnetization in different limits of the transverse field.
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 plateaux in two different cases of strong and weak rung couplings. With the strong rung coupling, the three magnetization plateaux are found at 1/3, 1/2, and 2/3 due to the frustration. Those can be understood in terms of a quasi-spinon 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 plateaux at 1/3 and 2/3 can be associated with the array of quasi-spinons such as soliton lattice. This is different from the usual Bose-Einstein-condensation picture of triplons. Our results will be useful to understand magnetization curves in BiCu2PO6.