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ABSTRACT: The low energy behaviour of the two-dimensional antiferromagnetic Heisenberg model is studied in the sector with total spins
S = 0,1,2 by means of a renormalization group procedure, which generates a recursion formula for the interaction matrix ΔS
(n+1) of 4 neighbouring “n clusters” of size 2n × 2n, n = 1,2,3,... from the corresponding quantities ΔS
(n). Conservation of total spin S is implemented explicitly and plays an important role. It is shown, how the ground state energies
ES
(n+1), S = 0,1,2 approach each other for increasing n, i.e. system size. The most relevant couplings in the interaction matrices
are generated by the transitions 〈S’,m’;n+1|Sq
*|S,m;n+1〉 between the ground states |S,m;n+1〉 (m = -S,...,S) on an (n+1)-cluster of size 2n+1 × 2n+1, mediated by the staggered spin operator Sq
*.
Physics of Condensed Matter 04/2012; 72(4):541-558. · 1.53 Impact Factor
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ABSTRACT: We study the magnetisation process of the one-dimensional spin-1/2 antiferromagnetic Heisenberg model with modulated couplings
over j=1,2,3sites. It turns out that the evolution of magnetisation plateaus depends on j and on the wave number q of the modulation according to the rule of Oshikawa et al. A mapping of two- and three-leg zig-zag ladders on one-dimensional systems with modulated couplings yields predictions for
the occurrence of magnetization plateaus. The latter are tested by numerical computations with the DMRG algorithm.
PACS. 75.10.-b General theory and models of magnetic ordering - 75.10.Jm Quantized spin models - 75.45.+j Macroscopic quantum
phenomena in magnetic systems
Physics of Condensed Matter 04/2012; 15(3):475-481. · 1.53 Impact Factor
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ABSTRACT: The low energy behaviour of the 2d antiferromagnetic Heisenberg model is studied in the sector with total spins $S=0,1,2$ by means of a renormalization group procedure, which generates a recursion formula for the interaction matrix $\Delta_S^{(n+1)}$ of 4 neighbouring "$n$ clusters" of size $2^n\times 2^n$, $n=1,2,3,...$ from the corresponding quantities $\Delta_S^{(n)}$. Conservation of total spin $S$ is implemented explicitly and plays an important role. It is shown, how the ground state energies $E_S^{(n+1)}$, $S=0,1,2$ approach each other for increasing $n$, i.e. system size. The most relevant couplings in the interaction matrices are generated by the transitions $<S',m';n+1|S_q^*|S,m;n+1>$ between the ground states $|S,m;n+1>$ ($m=-S,...,S$) on an $(n+1)$-cluster of size $2^{n+1}\times 2^{n+1}$, mediated by the staggered spin operator $S_q^*$ Comment: 18 pages, 8 figures, RevTex
11/2008;
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ABSTRACT: A two-dimensional model of interacting plaquettes is studied by means of the real space renormalization group approach. Interactions between the plaquettes are mediated solely by spin excitations on the plaquettes. Depending on the plaquette-plaquette coupling $J$, we find two regimes: "confinement" $J_c< J\leq 1$, where the singlet ground state forms an infinite ("confined") cluster in the thermodynamical limit. Here the singlet-triplet gap vanishes, which is the signature for long range spin-spin correlators. "deconfinement" $0\leq J< J_c$, where the singlet ground state "deconfines" - i.e. factorizes - into finite $n$-clusters of size $2^n\times 2^n$, with $n\leq n_c(J)$. Here the singlet-triplet gap is finite. The critical value turns out to be $J_c=0.473528..$. Comment: 7 pages, 11 figures, RevTex, corrected typos
11/2008;
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ABSTRACT: We discuss numerical results for the 1 — D spin 1/2 antiferromagnetic Heisenberg model with next-to-nearest neighbour coupling in the presence of a uniform magnetic
field. The model develops zero frequency excitations at field-dependent soft-mode momenta. We compute critical quantities
from finite size dependence of static structure factors.
05/2007: pages 41-61;
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ABSTRACT: We investigate the critical exponents $\eta_3(\alpha,M), \eta_1(\alpha,M)$ associated with the singularities in the longitudinal and transverse structure factors of the one dimensional antiferromagnetic Heisenberg model with nearest (J_1) and next to nearest (J_2) neighbour coupling of relative strength $\alpha = {J_2}/{J_1}$ and an external field $B$ with magnetization $M(B)$. Comment: LaTeX file (text) + 7 PS files (figures)
02/1999;
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ABSTRACT: We study the one-dimensional spin-1/2 antiferromagnetic Heisenberg model exposed to an external field, which is a superposition
of a homogeneous field h3 and a small periodic field of strength h1. For the case of a transverse staggered field a gap opens, which scales with , where is given by the critical exponent defined through the transverse structure factor of the model at h
1
=0. For the case of a longitudinal periodic field with wave vector and strength hq a plateau is found in the magnetization curve at M=1/4. The difference of the upper- and lower magnetic field scales with , where is given by the critical exponent defined through the longitudinal structure factor of the model at h
q
=0.
Physics of Condensed Matter 12/1998; 7(2):225-231. · 1.53 Impact Factor
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ABSTRACT: The one-dimensional S = 1 quantum spin chain with a linear and bilinear nearest-neighbour interaction of equal strength is integrable by the nested Bethe ansatz. In this paper the model is studied in the presence of an external magnetic field and an internal crystal field. By solving the Bethe ansatz equations for chains up to length N = 360 we construct the complete phase diagram of the system. We discuss how the magnetization curves depend on the internal field. In the SU(3) phase, where all three densities of atoms with -component -1, 0, +1 are non-vanishing, lines of constant density can be approximately parametrized by modified hypocycloides.
Journal of Physics A General Physics 12/1998; 29(14):3951.
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ABSTRACT: On the basis of a numerical computation of the ground states in the sectors with a given total spin S we study the magnetic properties of the one-dimensional frustrated antiferromagnetic Heisenberg model at zero temperature and at the spin-fluid - dimer phase transition. We find that the magnetization curve M(B) has a quartic-root singularity near saturation, . The longitudinal spin - spin, the dimer - dimer and the transverse spin - spin structure factors develop singularities at the field-dependent momenta and , respectively. The type of each of these singularities depends on the frustration parameter and the magnetization M.
Journal of Physics Condensed Matter 12/1998; 8(5):553. · 2.55 Impact Factor
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ABSTRACT: We study the one-dimensional spin-1/2 model with nearest and next-to-nearest-neighbor couplings exposed to a homogeneous magnetic field $h_{3}$ and a dimer field with period $q$ and strength $\delta$. The latter generates a magnetization plateau at $M=(1-q/\pi)/2$, which evolves with strength $\delta$ of the perturbation as $\delta^{\epsilon}$, where $\epsilon=\epsilon(h_{3},\alpha)$ is related to the $\eta$-exponent which describes the critical behavior of the dimer structure factor, if the perturbation is switched of ($\delta=0$). We also discuss the appearance of magnetization plateaus in ladder systems with $l$ legs. Comment: to be published in Phys. Rev. B
10/1998;
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ABSTRACT: We study the one-dimensional spin-1/2 antiferromagnetic Heisenberg model exposed to an external field, which is a superposition of a homogeneous field $h_{3}$ and a small periodic field of strength $h_{1}$. For the case of a transverse staggered field a gap opens, which scales with $h_{1}^{\epsilon_{1}}$, where $\epsilon_{1}=\epsilon_{1}(h_{3})$ is given by the critical exponent $\eta_{1}(M(h_{3}))$ defined through the transverse structure factor of the model at $h_{1}=0$. For the case of a longitudinal periodic field with wave vector $q=\pi/2$ and strength $h_{q}$ a plateau is found in the magnetization curve at $M=1/4$. The difference of the upper- and lower magnetic field scales with $h_{3}^{u}-h_{3}^{l}\sim h_{q}^{\epsilon_{3}}$, where $\epsilon_{3}=\epsilon_{3}(h_{3})$ is given by the critical exponent $\eta_{3}(M(h_{3}))$ defined through the longitudinal structure factor of the model at $h_{q}=0$.
10/1998;
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ABSTRACT: We investigate the scaling properties of the excitation energies and transition amplitudes of the one-dimensional spin-$1\over 2$ antiferromagnetic Heisenberg model exposed to an external perturbation. Two types of perturbations are discussed in detail: a staggered field and a dimerized field. Comment: 10 pages, 6 figures, to be published in Euro. Phys. J. B, LaTeX-class svjour from Springer
06/1998;
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ABSTRACT: We study the first derivative of the staggered magnetization squared $dm^\dag(\theta)^2/d\theta$ and the second derivative $d^2e_0(\theta)/d\theta^2$ of the ground state energy per site. The parameter $\theta$ controls the anisotropy between horizontal and vertical couplings in a two-dimensional (2D) spin-1/2 antiferromagnetic Heisenberg model. It is shown, that both derivatives diverge at $\theta=1$, where the anisotropic 2D model reduces to the 1D model. Comment: 9 pages, ReVTeX with 8 figures, to be published in PRB
11/1997;
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ABSTRACT: We present numerical results on the zero temperature magnetization curve and the static structure factors of the two dimensional antiferromagnetic Heisenberg model in the presence of an external field. The impact of frustration is also studied.
Zeitschrift für Physik B Condensed Matter 07/1997; 104(1):117-123.
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ABSTRACT: We present numerical results on the zero temperature magnetization curve and the static structure factors of the two dimensional antiferromagnetic Heisenberg model in the presence of an external field. The impact of frustration is also studied. Comment: 6 pages, 16 figures, REVTEX
10/1996;
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ABSTRACT: The impact of the non-2-spinon excitations of the one-dimensional $S=1/2$ Heisenberg antiferromagnet on the integrated intensity, the susceptibility, the frequency moments, and the Euclidian time representation of the $T=0$ dynamic spin structure factor $S(q,\omega)$ is studied on the basis of finite-size data for chains with up to $N=28$ sites.
08/1996;
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ABSTRACT: We present results on the specific heat and the staggered magnetization of the three dimensional antiferromagnetic Heisenberg model. These results are obtained from a numerical solution of the approximated evolution equation for the expectation values of the Boltzmann factor between valence-bond states.
Zeitschrift für Physik B Condensed Matter 04/1996; 100(2):277-281.
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ABSTRACT: We compute the energies and transition probabilities for low excitations in the one dimensional antiferromagnetic spin-1/2 Heisenberg model by means of the recursion method. We analyse finite size effects in the euclidian time ($\tau$)-representation and compare the resulting estimate for the thermodynamical limit with two parametrizations for the dynamical structure factors in the spectral ($\omega$)-representation. Comment: PostScript file with 13 pages + 5 figures, uuencoded compressed
07/1995;
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ABSTRACT: The static structure factors of the XXZ model in the presence of uniform field are determined from an exact computation of the groundstates at given total spin on rings with $N=4,6,\ldots,28$ sites. In contrast to the naive expectation a weak uniform field strengthens the antiferromagnetic order in the transverse structure factor for the isotropic case. Comment: 8 pages RevTex 3.0, 11 Figueres, uuencoded file
10/1994;
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ABSTRACT: We perform a finite size analysis of the longitudinal and transverse structure factors $S_j(p,\gamma,N),j=1,3$ in the groundstate of the spin-$\frac{1}{2}$ XXZ model. Comparison with the exact results of Tonegawa for the XX model yields excellent agreement. Comparison with the conjecture of M\"uller, Thomas, Puga and Beck reveals discrepancies in the momentum dependence of the longitudinal structure factors. Comment: 9 pages RevTex 3.0 and 17 figures as uuencoded file
03/1994;
