Level Spectroscopy: Physical Meaning and Application to the Magnetization Plateau Problems

Okamoto, Ken‐ichi

doi:10.1143/ptps.145.113

Cited by 14 publications

(16 citation statements)

References 10 publications

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“…(13) As a numerical check, we have also performed the numerical diagonalization using the Lanczös method and the level spectroscopy analysis. [8][9][10][11] We found that the numerical results are in good agreement with the results of the perturbation theory as shown in Figs.3-8.…”

supporting

confidence: 84%

Inversion Phenomenon and Phase Diagram of theS=1/2 Distorted Diamond Chain with theXXZInteraction Anisotropy

Tokuno

Okamoto

2005

J. Phys. Soc. Jpn.

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We discuss the anisotropies of the Hamiltonian and the wave-function in an S = 1/2 distorted diamond chain. The ground-state phase diagram of this model is investigated using the degenerate perturbation theory up to the first order and the level spectroscopy analysis of the numerical diagonalization data. In some regions of the obtained phase diagram, the anisotropy of the Hamiltonian and that of the wave-function are inverted, which we call inversion phenomenon; the Néel phase appears for the XY -like anisotropy and the spin-fluid phase appears for the Ising-like anisotropy. Three key words are important for this nature, which are frustration, the trimer nature, and the XXZ anisotropy.

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supporting

confidence: 84%

Inversion Phenomenon and Phase Diagram of theS=1/2 Distorted Diamond Chain with theXXZInteraction Anisotropy

Tokuno

Okamoto

2005

J. Phys. Soc. Jpn.

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“…For the purpose of drawing the M = (2/3)M s plateau phase diagram, we have performed the numerical diagonalization of the finite size Hamiltonian by the Lanczos method. We can apply the LS method [19,26,27,34,35] to this kind of plateaufulplateauless transition of the BKT type [36,37,38,39] …”

Section: Magnetization Plateau At M = (2/3)m Smentioning

confidence: 99%

Magnetic properties of theS 1/2 distorted diamond chain atT 0

Okamoto

Tonegawa

Kaburagi

2003

J. Phys.: Condens. Matter

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105

115

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Abstract. We explore, at T = 0, the magnetic properties of the S = 1/2 antiferromagnetic distorted diamond chain described by the Hamiltonian H =, which well models A 3 Cu 3 (PO 4 ) 4 with A = Ca, Sr, Bi 4 Cu 3 V 2 O 14 and azurite Cu 3 (OH) 2 (CO 3 ) 2 . We employ the physical consideration, the degenerate perturbation theory, the level spectroscopy analysis of the numerical diagonalization data obtained by the Lanczos method and also the density matrix renormalization group (DMRG) method. We investigate the mechanisms of the magnetization plateaux at M = M s /3 and M = (2/3)M s , and also show the precise phase diagrams on the (J 2 /J 1 , J 3 /J 1 ) plane concerning with these magnetization plateaux, where M = N l=1 S z l and M s is the saturation magnetization. We also calculate the magnetization curves and the magnetization phase diagrams by means of the DMRG method.

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“…Amongst those, the most remarkable one is the necessity to understand the unusual new properties presented by low dimensional magnetic materials [1,2,3,4] at low temperature, which are described in terms of its many-body behaviour and its quantum transitions [5]. As manifestation of these properties we can mention the appearance of magnetization plateaus as functions of the external magnetic field [6,7], the existence of an energy gap between the ground state and first excited state at zero field [8] and the presence of quantum critical behaviour [4,9,10].…”

Section: Introductionmentioning

confidence: 99%

The isotropic model on the inhomogeneous periodic chain

Lima¹,

Alves²,

Gonçalves³

2006

Journal of Magnetism and Magnetic Materials

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The static and dynamic properties of the isotropic XY-model (s = 1/2) on the inhomogeneous periodic chain, composed of N segments with n different exchange interactions and magnetic moments, in a transverse field h are obtained exactly at arbitrary temperatures. The properties are determined by introducing the generalized Jordan-Wigner transformation and by reducing the problem to a diagonalization of a finite matrix of n-th order. The diagonalization procedure is discussed in detail and the critical behaviour induced by the transverse field, at T = 0, is presented. The quantum transitions are determined by analyzing the behaviour of the induced magnetization, defined as (1/n) n m=1 µ m < S z j,m > where µ m is the magnetic moment at site m within the segment j, as a function of the field, and the critical fields determined exactly. The dynamic correlations, < S z j,m (t)S z j ′ ,m ′ (0) >, and the dynamic susceptibility χ zz q (ω) are also obtained at arbitrary temperatures. Explicit results are also presented in the limit T = 0, where the critical behaviour occurs, for the static susceptibility χ zz q (0) as a function of the transverse field h, and for the frequency dependency of dynamic susceptibility χ zz q (ω). Also in this limit, the transverse time-correlation < S x j,m (t)S x j ′ ,m ′ (0) >, the dynamic and isothermal susceptibilities, χ xx q (ω) and χ xx T , are obtained for the transverse field greater or equal than the saturation field.

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Level Spectroscopy: Physical Meaning and Application to the Magnetization Plateau Problems

Abstract: We review the level spectroscopy, which is a powerful method of analyzing the numerical data with respect to the Berezinskii-Kosterlitz-Thouless quantum phase transition in one dimension. We focus on its physical meaning and also its application to the magnetization plateau problems. * )

Cited by 14 publications

References 10 publications

Inversion Phenomenon and Phase Diagram of theS=1/2 Distorted Diamond Chain with theXXZInteraction Anisotropy

Inversion Phenomenon and Phase Diagram of theS=1/2 Distorted Diamond Chain with theXXZInteraction Anisotropy

Magnetic properties of theS 1/2 distorted diamond chain atT 0

The isotropic model on the inhomogeneous periodic chain

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