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

Cusp Singularity in the Magnetization Curve of 1D Quantum Spin Systems

Kouichi Okunishi

Published Jan 1, 2002• 5 citations
Publisher

Abstract

We give a short review of the cusp singularity in the magnetization curve of 1D quantum spin systems. We show that the cusp singularity appears for a certain class of nonintegrable frustrated spin systems, using the density matrix renormaziation group method. We also discuss the cusp appearance mechanism on the basis of the one particle dispersion curve of the elementary excitation, where the shape change of the dispersion curve induced by the frustrated interaction plays an essential role.

DOI
10.1143/ptps.145.119

Related papers

Middle-field cusp singularities in the magnetization process of one-dimensional quantum antiferromagnets

Kouichi Okunishi, Yasuhiro Hieida, Yasuhiro Akutsu

We study the zero-temperature magnetization process $(M\ensuremath{-}H$ curve) of one-dimensional quantum antiferromagnets using a variant of the density-matrix renormalization group method. For both the $S=1/2$ zig-zag spin ladder and the $S=1$ bilinear-biquadratic chain, we find clear cusp-type singularities in the middle-field region of the $M\ensuremath{-}H$ curve. These singularities are successfully explained in terms of the double-minimum shape of the energy dispersion of the low-lying excitations. For the $S=1/2$ zig-zag spin ladder, we find that the cusp formation accompanies the Fermi-liquid to non-Fermi-liquid transition.

arXiv:cond-mat/9904155•Physical review. B, Condensed matter•Sep 1, 1999•58 citations

Cusp Singularities in the Magnetization Curve of Frustrated Kondo Necklace Model

Takahiro Yamamoto, Rumi Manago, Yoshihiro Mori +1 more

Magnetization processes of frustrated Kondo necklace model are studied by means of a density matrix renormalization group (DMRG) method and an elementary band theory based on a bond-operator formalism. The DMRG calculations clearly show the cusp singularity in a low-magnetization region ($0

arXiv:cond-mat/0204588•Journal of the Physical Society of Japan•Dec 15, 2003•9 citations

Magnetization of CuGeO3

Suyan Li

As the first inorganic spin-Peierls compound, CuGe03 can be described with an AF Heisenberg model. The magnetization process of CuGe03 is studied using the numerical Density Matrix Renormalization Group (DMRG) technique. The M - H curve of CuGe03 and other one dimensional Heisenberg systems are described, and their different nature are analyzed. In particular, the middle field cusp singularity appears in the M- H curve of CuGe03 is described.

•Sep 1, 2005•0 citations

Magnetic Phase Diagram of theS=1/2 Antiferromagnetic Zigzag Spin Chain in the Strongly Frustrated Region: Cusp and Plateau

Kouichi Okunishi, Takashi Tonegawa

We determine the magnetic phase diagram of the antiferromagnetic(AF) zigzag spin chain in the strongly frustrated region, using the density matrix renormalization group method. We find the magnetization plateau at 1/3 of the full moment accompanying the spontaneous symmetry breaking of the translation, the cusp singularities above and/or below the plateau, and the even-odd effect in the magnetization curve. We also discuss the formation mechanisms of the plateau and cusps briefly.

arXiv:cond-mat/0211458•Journal of the Physical Society of Japan•Mar 15, 2003•96 citations

Magnetic properties of the one-dimensional multicomponent spin-gap system

Akira Kawaguchi, Tatsuya Fujii, Norio Kawakami

Magnetic properties of a one-dimensional multicomponent quantum-spin system with an excitation gap are studied based on the integrable spin model introduced by Bariev et al. [Z. Phys. B 96, 395 (1995)]. By exactly computing the magnetization, we show how a characteristic structure with plateaus and cusps appears in the magnetization process. To study the low-energy dynamics of the system, we apply a finite-size scaling analysis to the excitation spectrum, and thereby evaluate the power-law exponent as well as the enhancement factor for the low-temperature NMR relaxation rate ${1/T}_{1}.$ We discuss the critical properties of ${1/T}_{1}$ around plateaus and cusps in the magnetization curve.

arXiv:cond-mat/0101423•Physical review. B, Condensed matter•Mar 19, 2001•4 citations

Anomalous magnetization process in frustrated spin ladders

Tôru Sakai, Kiyomi Okamoto, Kouichi Okunishi +1 more

We study, at T = 0, the anomalies in the magnetization curve of the S = 1 two-leg ladder with frustrated interactions. We focus mainly on the existence of the M = M s /2 plateau, where M s is the saturation magnetization. We report the results using the degenerate perturbation theory and the density matrix renormalization group, which lead to consistent conclusion with each other. We also touch on the M = M s /4 and (3/4) M s plateaux and cusps.

arXiv:cond-mat/0308473•Journal of Physics Condensed Matter•Mar 4, 2004•4 citations
We give a short review of the cusp singularity in the magnetization curve of 1D quantum spin systems. We show that the cusp singularity appears for a certain class of nonintegrable frustrated spin systems, using the density matrix renormaziation group method. We also discuss the cusp appearance mechanism on the basis of the one particle dispersion curve of the elementary excitation, where the shape change of the dispersion curve induced by the frustrated interaction plays an essential role.
We study the zero-temperature magnetization process $(M\ensuremath{-}H$ curve) of one-dimensional quantum antiferromagnets using a variant of the density-matrix renormalization group method. For both the S=1/2S=1/2S=1/2 zig-zag spin ladder and the S=1S=1S=1 bilinear-biquadratic chain, we find clear cusp-type singularities in the middle-field region of the $M\ensuremath{-}H$ curve. These singularities are successfully explained in terms of the double-minimum shape of the energy dispersion of the low-lying excitations. For the S=1/2S=1/2S=1/2 zig-zag spin ladder, we find that the cusp formation accompanies the Fermi-liquid to non-Fermi-liquid transition.
Magnetic properties of a one-dimensional multicomponent quantum-spin system with an excitation gap are studied based on the integrable spin model introduced by Bariev et al. [Z. Phys. B 96, 395 (1995)]. By exactly computing the magnetization, we show how a characteristic structure with plateaus and cusps appears in the magnetization process. To study the low-energy dynamics of the system, we apply a finite-size scaling analysis to the excitation spectrum, and thereby evaluate the power-law exponent as well as the enhancement factor for the low-temperature NMR relaxation rate 1/T1.{1/T}_{1}.1/T1​. We discuss the critical properties of 1/T1{1/T}_{1}1/T1​ around plateaus and cusps in the magnetization curve.