Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Progress of Theoretical Physics Supplement

Magnetization Plateaus of Frustrated Kondo Necklace Model

Takahiro Yamamoto, Chikara Ishii

Published Jan 1, 2002• 1 citation
Publisher

Abstract

The magnetization plateaus of frustrated Kondo necklace model have been studied with use of the bosonization technique and level spectroscopy method. It is shown that the model may show three phases (dimer plateau, Néel plateau and Tomonaga-Luttinger liquid phases) due to competitions among Ising anisotropy Δ, the nearest and next nearest neighbor exchange interactions J1, J2. It is shown from bosonization technique that quantum transition between the dimer and Néel plateaus is Gaussian type, while the transition from one of these plateau phases to Tomonaga-Luttinger phase is Brezinskii-Kosterlitz-Thouless type. The phase diagram is constructed on the Δ-J2/J1 plane with use of level spectroscopy method, under the condition that the system has a half of the saturation magnetization.

DOI
10.1143/ptps.145.64

Related papers

Phase diagram and critical properties of the frustrated Kondo necklace model in a magnetic field

Takahiro Yamamoto, Kôichirô Ide, Chikara Ishii

The critical properties of the frustrated Kondo necklace model with a half saturation magnetization $(m=1/2)$ have been studied by means of an exact-diagonalization method. It is shown from bosonization technique that the model can be effectively expressed as a quantum sine-Gordon model. Thus it may show three (dimer plateau, N\'eel plateau and Tomonaga-Luttinger liquid) phases due to competitions among the Ising anisotropy $\ensuremath{\Delta},$ and the nearest- and next-nearest-neighbor exchange interactions ${J}_{1}$ and ${J}_{2}.$ The boundary lines on the $\ensuremath{\Delta}$-${J}_{2}{/J}_{1}$ phase diagram separating the three phases are determined by the method of level spectroscopy, based on the conformal field theory.

arXiv:cond-mat/0204174•Physical review. B, Condensed matter•Sep 9, 2002•9 citations

Magnetization Process of One-Dimensional Kondo Necklace Model with Next-Nearest-Neighbor Interaction

Takahiro Yamamoto, Masanari Asano, Chikara Ishii

The magnetization process of one-dimensional Kondo necklace model with next-nearest-neighbor interaction has been studied by the use of exact-diagonalization method. The magnetization plateaus appear at zero ( m =0) and at half ( m =1/2) of the saturation magnetization. The ground state in the absence of a magnetic field is regarded as an aggregate of intra-atomic Kondo singlets. On the other hand, the spin configuration at the 1/2-plateau represents the intra-chain dimer (σ-dimer) phase with broken translational symmetry. The picture for spin configurations in the uniform magnetic fields other than m =0 and 1/2 are also given. We also determined the phase diagram for the ground state of the system in the magnetic field.

Journal of the Physical Society of Japan•Dec 15, 2001•5 citations

Tomonaga–Luttinger Spin Liquid and Kosterlitz–Thouless Transition in the Spin-1/2 Branched Chains: The Study of Topological Phase Transition

Hamid Arian Zad, Azam Zoshki, N.S. Ananikian +1 more

In the present work, we provide a comprehensive numerical investigation of the magnetic properties and phase spectra of three types of spin-1/2 branched chains consisting of one, two and three side spins per unit block with intra-chain interaction and a uniform inter-chain interaction in the presence of an external magnetic field. In a specific magnetic field interval, the low-temperature magnetization of these chains shows a step-like behavior with a pronounced plateau depending on the strength and the type of intra-chain interaction being ferromagnetic or antiferromagnetic. We demonstrate that when inter-chain interaction J1 is antiferromagnetic and intra-chain interaction J2 is ferromagnetic, the magnetization of the models manifests a smooth increase without a plateau, which is evidence of the existence of a Luttinger-like spin liquid phase before reaching its saturation value. On the other hand, when J1 is ferromagnetic and J2 is antiferromagnetic, the low-temperature magnetization of the chain with two branches shows an intermediate plateau at one-half of the saturation magnetization that breaks a quantum spin liquid phase into two regions. The magnetization of the chain with three branches exhibits two intermediate plateaus and two regions of a quantum spin liquid. We demonstrate that the chains with more than one side spin illustrate in their ground-state phase diagram a Kosterlitz-Thouless transition from a gapful phase to a gapless spin liquid phase.

Materials•Jun 13, 2022•2 citations

Inhomogeneous superconducting phases in the frustrated Kondo-Heisenberg chain

A. Dobry, Akbar Jaefari, Eduardo Fradkin

We use bosonization and renormalization group methods to determine the ground-state phase diagram of a one-dimensional frustrated Kondo-Heisenberg system consisting of a one-dimensional spin-$\frac{1}{2}$ Luttinger liquid coupled by a Kondo exchange interaction ${J}_{K}$ to a frustrated quantum antiferromagnetic Heisenberg chain, with a nearest-neighbor exchange coupling ${J}_{1}$ and a next-nearest-neighbor (frustrating) exchange interaction ${J}_{2}$. We analyze the interplay of quantum frustration in the antiferromagnetic chain with the Kondo exchange coupling ${J}_{K}$ with the Luttinger liquid. We discuss the structure of the phase diagram of this system as a function of the ratios ${J}_{K}/{J}_{1}$, ${J}_{2}/{J}_{1}$, and of the parameters of the Luttinger liquid. In particular, we discuss in detail the regimes in which a pair-density-wave state may be realized and its relation with the spin correlations in the frustrated antiferromagnetic chain.

arXiv:1304.5256•Physical Review B•Jun 7, 2013•8 citations

Quantum vs Classical Magnetization Plateaus of S=1/2 Frustrated Heisenberg Chains

Kazuo Hida, Ian K. Affleck

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.

arXiv:cond-mat/0501697•Journal of the Physical Society of Japan•Jun 1, 2005•46 citations

Magnetization Plateau in the Frustrated Alternating Spin Chain

Tetsuji Kuramoto

We study the magnetization plateau at m =1/2 in the S =1/2 and S =1 alternating spin Heisenberg chain with two next-nearest-neighbor (NNN) interactions J a between neighboring S =1/2 spins and J b between neighboring S =1 spins, using the numerical diagonalization and the density-matrix renormalization group (DMRG) method. We present the m =1/2 plateau phase diagram in the J a – J b plane obtained by the level crossing method useful for the Berezinskii–Kosterlitz–Thouless (BKT) transition. In this phase diagram, we find that there are two plateau phases distinguished by a parity of the alternating spin chain.

Journal of the Physical Society of Japan•Sep 15, 2004•1 citation
The magnetization plateaus of frustrated Kondo necklace model have been studied with use of the bosonization technique and level spectroscopy method. It is shown that the model may show three phases (dimer plateau, Néel plateau and Tomonaga-Luttinger liquid phases) due to competitions among Ising anisotropy Δ, the nearest and next nearest neighbor exchange interactions J1, J2. It is shown from bosonization technique that quantum transition between the dimer and Néel plateaus is Gaussian type, while the transition from one of these plateau phases to Tomonaga-Luttinger phase is Brezinskii-Kosterlitz-Thouless type. The phase diagram is constructed on the Δ-J2/J1 plane with use of level spectroscopy method, under the condition that the system has a half of the saturation magnetization.
The critical properties of the frustrated Kondo necklace model with a half saturation magnetization (m=1/2)(m=1/2)(m=1/2) have been studied by means of an exact-diagonalization method. It is shown from bosonization technique that the model can be effectively expressed as a quantum sine-Gordon model. Thus it may show three (dimer plateau, N\'eel plateau and Tomonaga-Luttinger liquid) phases due to competitions among the Ising anisotropy $\ensuremath{\Delta},$ and the nearest- and next-nearest-neighbor exchange interactions J1{J}_{1}J1​ and J2.{J}_{2}.J2​. The boundary lines on the $\ensuremath{\Delta}$-J2/J1{J}_{2}{/J}_{1}J2​/J1​ phase diagram separating the three phases are determined by the method of level spectroscopy, based on the conformal field theory.
The magnetization process of one-dimensional Kondo necklace model with next-nearest-neighbor interaction has been studied by the use of exact-diagonalization method. The magnetization plateaus appear at zero ( m =0) and at half ( m =1/2) of the saturation magnetization. The ground state in the absence of a magnetic field is regarded as an aggregate of intra-atomic Kondo singlets. On the other hand, the spin configuration at the 1/2-plateau represents the intra-chain dimer (σ-dimer) phase with broken translational symmetry. The picture for spin configurations in the uniform magnetic fields other than m =0 and 1/2 are also given. We also determined the phase diagram for the ground state of the system in the magnetic field.
In the present work, we provide a comprehensive numerical investigation of the magnetic properties and phase spectra of three types of spin-1/2 branched chains consisting of one, two and three side spins per unit block with intra-chain interaction and a uniform inter-chain interaction in the presence of an external magnetic field. In a specific magnetic field interval, the low-temperature magnetization of these chains shows a step-like behavior with a pronounced plateau depending on the strength and the type of intra-chain interaction being ferromagnetic or antiferromagnetic. We demonstrate that when inter-chain interaction J1 is antiferromagnetic and intra-chain interaction J2 is ferromagnetic, the magnetization of the models manifests a smooth increase without a plateau, which is evidence of the existence of a Luttinger-like spin liquid phase before reaching its saturation value. On the other hand, when J1 is ferromagnetic and J2 is antiferromagnetic, the low-temperature magnetization of the chain with two branches shows an intermediate plateau at one-half of the saturation magnetization that breaks a quantum spin liquid phase into two regions. The magnetization of the chain with three branches exhibits two intermediate plateaus and two regions of a quantum spin liquid. We demonstrate that the chains with more than one side spin illustrate in their ground-state phase diagram a Kosterlitz-Thouless transition from a gapful phase to a gapless spin liquid phase.
We use bosonization and renormalization group methods to determine the ground-state phase diagram of a one-dimensional frustrated Kondo-Heisenberg system consisting of a one-dimensional spin-12\frac{1}{2}21​ Luttinger liquid coupled by a Kondo exchange interaction JK{J}_{K}JK​ to a frustrated quantum antiferromagnetic Heisenberg chain, with a nearest-neighbor exchange coupling J1{J}_{1}J1​ and a next-nearest-neighbor (frustrating) exchange interaction J2{J}_{2}J2​. We analyze the interplay of quantum frustration in the antiferromagnetic chain with the Kondo exchange coupling JK{J}_{K}JK​ with the Luttinger liquid. We discuss the structure of the phase diagram of this system as a function of the ratios JK/J1{J}_{K}/{J}_{1}JK​/J1​, J2/J1{J}_{2}/{J}_{1}J2​/J1​, and of the parameters of the Luttinger liquid. In particular, we discuss in detail the regimes in which a pair-density-wave state may be realized and its relation with the spin correlations in the frustrated antiferromagnetic chain.
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.
We study the magnetization plateau at m =1/2 in the S =1/2 and S =1 alternating spin Heisenberg chain with two next-nearest-neighbor (NNN) interactions J a between neighboring S =1/2 spins and J b between neighboring S =1 spins, using the numerical diagonalization and the density-matrix renormalization group (DMRG) method. We present the m =1/2 plateau phase diagram in the J a – J b plane obtained by the level crossing method useful for the Berezinskii–Kosterlitz–Thouless (BKT) transition. In this phase diagram, we find that there are two plateau phases distinguished by a parity of the alternating spin chain.