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Progress of Theoretical Physics Supplement

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

Kazuo Hida, Ian K. Affleck

Published Jan 1, 2005• 0 citations
Publisher

Abstract

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.

DOI
10.1143/ptps.159.260

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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 competition between quantum and classical magnetization plateaus of S=1/2 frustrated Heisenberg chains with modified exchange couplings is investigated. The conventional S=1/2 frustrated Heisenberg chains is known to exhibit a 3-fold degenerate udu-type classical plateau at 1/3 of the saturation magnetization accompanied by the spontaneous Z_3 translational symmetry breakdown. The stability of this plateau phase against period 3 exchange modulation which favors the 00u-type quantum plateau state (00= singlet dimer) is studied by bosonization, renormalization group and numerical diagonalization methods. The ground state phase diagram and the spin configuration in each phase are numerically determined. The translationally invariant Valence Bond Solid-type model with 4-spin and third neighbor interactions, which has the exact 00u-type quantum plateau state, is also presented. The phase transition to the classical udu-type ground state is also observed by varying the strength of 4-spin and third neighbor interactions. The relation between these two types of models with quantum plateau states is discussed.
The ground state properties of the S = 1/ 2 frustrated Heisenberg chain with period 3 exchange modulation are investigated using the numerical diagonalization and density matrix renormalization group (DMRG) method. It is known that this model has a magnetization plateau at one third of the saturation magnetization Ms. On the other hand, the ground state is ferrimagnetic even in the absence of frustration if one of the nearest neighbour bond is ferromagnetic and the others are antiferromagnetic. In the present work, we show that this ferrimagnetic state continues to the region in which all bonds are antiferromagnetic if the frustration is strong. This state further continues to the above- mentioned 1/ 3 plateau state. In between, we also find the noncollinear ferrimagnetic phase in which the spontaneous magnetization is finite but less than Ms/ 3. The intuitive interpretation for the phase diagram is given and the physical properties of these phases are discussed.
The ground state properties of the S = 1/2 frustrated Heisenberg chain with period 3 exchange modulation are investigated using the numerical diagonalization and density matrix renormalization group (DMRG) method. It is known that this model has a magnetization plateau at one third of the saturation magnetization M s . On the other hand, the ground state is ferrimagnetic even in the absence of frustration if one of the nearest neighbour bond is ferromagnetic and the others are antiferromagnetic. In the present work, we show that this ferrimagnetic state continues to the region in which all bonds are antiferromagnetic if the frustration is strong. This state further continues to the above-mentioned 1/3 plateau state. In between, we also find the noncollinear ferrimagnetic phase in which the spontaneous magnetization is finite but less than M s /3. The intuitive interpretation for the phase diagram is given and the physical properties of these phases are discussed.
We consider the spin-1/2 Heisenberg chain with alternating spin exchange in the presence of additional modulation of exchange on odd bonds with period 3. We study the ground state magnetic phase diagram of this hexamer spin chain in the limit of very strong antiferromagnetic (AF) exchange on odd bonds using the numerical Lanczos method and bosonization approach. In the limit of strong magnetic field commensurate with the dominating AF exchange, the model is mapped onto an effective XXZ Heisenberg chain in the presence of uniform and spatially modulated fields, which is studied using the standard continuum-limit bosonization approach. In the absence of additional hexamer modulation, the model undergoes a quantum phase transition from a gapped phase into the only one gapless Lüttinger liquid (LL) phase by increasing the magnetic field. In the presence of hexamer modulation, two new gapped phases are identified in the ground state at magnetization equal to [Formula: see text] and [Formula: see text] of the saturation value. These phases reveal themselves also in the magnetization curve as plateaus at corresponding values of magnetization. As a result, the magnetic phase diagram of the hexamer chain shows seven different quantum phases, four gapped and three gapless, and the system is characterized by six critical fields which mark quantum phase transitions between the ordered gapped and the LL gapless phases.
We investigate the S=1S=1S=1 antiferromagnetic quantum spin chain with the exchange and single-ion anisotropies in a magnetic field, using numerical exact diagonalization of finite-size clusters, level spectroscopy analysis, and the density matrix renormalization group (DMRG). We find that a translational symmetry broken magnetization plateau possibly appears at the half of the saturation magnetization, when the anisotropies compete with each other. The level spectroscopy analysis gives the phase diagram at half the saturation magnetization. The DMRG calculation presents the magnetization curves for some typical parameters and clarifies the spin structure in the plateau phase.