Low-dimensional quantum antiferromagnetic Heisenberg model studied using Wigner-Jordan transformations

Yr, Wang

doi:10.1103/physrevb.46.151

Cited by 55 publications

(48 citation statements)

References 44 publications

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“…To answer this question we have developed a mean field (MF) theory which maps the system onto a random phase XY model. Under a 2D Wigner-Jordan transformation [28], one can relate a particle creation operator with a spin operator for the spin-1͞2 system: c Under this transformation, Eq. (1) is mapped to a spin Hamiltonian,…”

Section: -9007͞98͞80(16)͞3563(4)$1500mentioning

confidence: 99%

Kosterlitz-Thouless-Type Metal-Insulator Transition of a 2D Electron Gas in a Random Magnetic Field

1998

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We study the localization property of a two-dimensional noninteracting electron gas in the presence of a random magnetic field. The localization length is directly calculated using a transfer matrix technique and finite size scaling analysis. We show strong numerical evidence that the system undergoes a disorder-driven Kosterlitz-Thouless-type metal-insulator transition. We develop a mean field theory which maps the random field system into a two-dimensional XY model. The vortex and antivortex excitations in the XY model correspond to two different kinds of magnetic domains in the random field system. [ S0031-9007(98) There has been a long lasting interest in understanding the localization problem in two-dimensional (2D) systems. According to the scaling theory of localization [1], all states in a 2D system are localized if only scalar random potential is present. However, in the presence of a strong perpendicular magnetic field, where the time reversal symmetry is broken, extended states appear in the center of disorder-broadened Landau bands and give rise to the integer quantum Hall effect (QHE) [2].Recently, Halperin, Lee, and Read [3] and Kalmeyer and Zhang [4] developed an effective Chern-Simons field theory to understand electronic properties of the fractional QHE systems. In their theory the quasiparticles are weakly interacting composite fermions [5] which can be constructed by attaching an even number of flux quanta to electrons under a Chern-Simons transformation. In this simple picture, the fractional QHE can be mapped into the integer QHE for the composite fermion system subject to an effective magnetic field [5]. At the filling factor n f 1 2 , although the effective magnetic field B ‫ء‬ vanishes, composite fermions are subject to the random fluctuations of the gauge field induced by the ordinary impurities [3,4]. Thus, it is important to study the localization properties of noninteracting charged particles in the presence of a random magnetic field to understand the half-filling system. The problem of charged particles moving in a random magnetic field is also relevant to the theoretical studies of high T c models where the gauge field fluctuations play an important role [6].There have been many studies trying to understand the localization problem of noninteracting particles in a random magnetic field with zero mean [7][8][9][10][11][12][13][14][15][16][17][18]. However, the main issue, namely, whether there is metal-insulator transition (MIT), remains controversial. Conclusions from previous numerical studies can be summarized into the following three classes: (i) There exists a MIT with scaling behavior on both metal and insulator sides [15,18], (ii) there exists a MIT; however, the scaling curve is found only on the insulator side [7,8,13], and (iii) all states are localized [9,10]. On the analytic side, the result is also inconclusive. According to the conventional scaling theory of localization, the random flux system belongs to the unitary ensemble, which is described by a nonlinear sigma mo...

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Section: -9007͞98͞80(16)͞3563(4)$1500mentioning

confidence: 99%

Kosterlitz-Thouless-Type Metal-Insulator Transition of a 2D Electron Gas in a Random Magnetic Field

1998

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“…The spin operators may be represented as fermions by use of the 2D JW transformation, which has the advantage that all spin commutation relations, as well as the so called spin on-site exclusion principle are automatically preserved [15]. This method has been proved well for application to real materials [15,9].…”

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confidence: 99%

“…[14,15,17]) where the phase factor e iψ i,j has alternative values e iπ and 1, i.e., it varies with (−1) i+j (note that this coincides with the above dimerization pattern). This configuration ensures that each elementary plaquette encloses a net flux of π [14,15]. Then the Hamiltonian can be rewritten as follows in terms of fermion operators e and f corresponding to the two sublattices A and B respectively (constants irrelevant to δ are ignored)…”

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confidence: 99%

“…This method has been proved well for application to real materials [15,9]. For concreteness, the following formulas are adopted [16,17] …”

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confidence: 99%

“…Usually the effect of interchain coupling is underestimated in this way. Here, the two-dimensional (2D) Jordan-Wigner (JW) transformation [14][15][16][17]9] is adopted so that the intrachain and interchain exchanges may be treated on an equal footing from the beginning.…”

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confidence: 99%

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Spin-Peierls transition in an anisotropic two-dimensionalXYmodel

2001

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The two-dimensional Jordan-Wigner transformation is used to investigate the zero temperature spin-Peierls transition for an anisotropic two-dimensional XY model in adiabatic limit. The phase diagram between the dimerized (D) state and uniform (U) state is shown in the parameter space of dimensionless interchain coupling h (= J ⊥ /J) and spin-lattice coupling η. It is found that the spin-lattice coupling η must exceed some critical value η c in order to reach the D phase for any finite h. The dependence of η c on h is given by −1/ ln h for h → 0 and the transition between U and D phase is of first-order for at least h > 10 −3 .

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A Coherent-State Representation of the Ground State of Quantum Antiferromagnets

Cabrera

1994

New Trends in Magnetism, Magnetic Materials, and Their Applications

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Low-dimensional quantum antiferromagnetic Heisenberg model studied using Wigner-Jordan transformations

Cited by 55 publications

References 44 publications

Kosterlitz-Thouless-Type Metal-Insulator Transition of a 2D Electron Gas in a Random Magnetic Field

Kosterlitz-Thouless-Type Metal-Insulator Transition of a 2D Electron Gas in a Random Magnetic Field

Spin-Peierls transition in an anisotropic two-dimensionalXYmodel

A Coherent-State Representation of the Ground State of Quantum Antiferromagnets

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