Checkerboard-spin liquid-stripe state continuous transition in a frustrated Heisenberg antiferromagnet on a square lattice

Барабанов, А. Ф.; Beresovsky, V.M.

doi:10.1016/0375-9601(94)90942-3

Cited by 38 publications

(9 citation statements)

References 12 publications

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“…Recently, similar problems of frustrated antiferromagnetic Heisenberg systems have been studied in Refs. [21][22][23][24] where effect of the quantum fluctuations is also important.…”

Section: Discussionmentioning

confidence: 99%

Effect of frustrations on magnetism in the Ru double perovskiteSr2YRuO6

Кузьмин¹,

Овчинников

Singh

2003

Phys. Rev. B

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Localized Ru 5ϩ spins in Sr 2 YRuO 6 form a fcc lattice with an antiferromagnetic ͑AFM͒ nearest-neighbor ͑NN͒ coupling JϷ25 meV and rather low Néel temperature T N ϭ26 K. Analysis of the electronic structure of Sr 2 RuO 4 results in the effective Heisenberg model. We have studied the effect of frustrations on the AFM type-I structure of Sr 2 YRuO 6 in the spin-wave approximation. In the model with only NN coupling the AFM state is unstable due to frustrations, and T N ϭ0. Stabilization of the AFM state occurs due to the next-nearestneighbor coupling I or due to the magnetic anisotropy D. Very small values D/JϳI/Jр10 Ϫ3 are enough to obtain the experimental values of T N and sublattice magnetization mϭ1.85 B /Ru ͑62% from the nominal S ϭ3/2 value͒.

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“…Recently, similar problems of frustrated antiferromagnetic Heisenberg systems have been studied in Refs. [21][22][23][24] where effect of the quantum fluctuations is also important.…”

Section: Discussionmentioning

confidence: 99%

Effect of frustrations on magnetism in the Ru double perovskiteSr2YRuO6

Кузьмин¹,

Овчинников

Singh

2003

Phys. Rev. B

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“…(21) and (22), are depicted. Here, for the sake of comparison, we also present results from other works [18,24,[26][27][28][29]33]. The left curves correspond to the Néel antiferromagnetic ordering, and the right ones to the collinear stripe antiferromagnetic ordering.…”

Section: Results Of Numerical Calculations and Conclusionmentioning

confidence: 93%

“…2. Dependences of sublattice magnetizations on the parameter 2 / 1 at ′ 1 = 1 obtained in various approaches: our calculations (1 ); four-particle-cluster approximation [24] (2 ), sixteen-particle-cluster approximation [24] (3 ), finite-size scaling of exact diagonalization data [33] (4 ), density-matrix renormalization group method [18] (5 ), extrapolation of the data of coupled-cluster method [29] 6, and methods based on Green's functions: [26] 7, [27] (8 ), and [28] (9 ) limit, for the case of different antiferromagnetic orderings,…”

Section: Jordan-wigner Fermionization Mean-field-like Approximationmentioning

confidence: 99%

“…There are a lot of theoretical approaches to study quantum-mechanical spin systems with frustrations. For instance, the spin-1/2 1 − 2 antiferromagnetic Heisenberg model on a square lattice was consid-ered, in particular, by using the high-temperature expansion [5], density-matrix renormalization group method [18,21], and quantum Monte-Carlo method [22], in the cluster approximation [24] and the variational approach [25], on the basis of Green's function theory [26][27][28], as well as using the methods of coupled clusters [29][30][31] and exact diagonalization [32,33]. Each of the approaches has its shortcomings.…”

Section: Introductionmentioning

confidence: 99%

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Two-Dimensional Spin-1/2 J1 – J'1 – J2 Heisenberg Model within Jordan–Wigner Transformation

Baran

Verkholyak

2016

Ukr. J. Phys.

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The Jordan-Wigner transformation is applied to the spatially anisotropic spin-1/2 Heisenberg model on a square lattice with the nearest-neighbor and next-nearest-neighbor antiferromagnetic interactions. The transformed Hamiltonian describes the interacting spinless fermions that hop between neighbor sites in a gauge field. Using the mean-field-type approximation to both the direct interaction between fermions and the phase factors, which represent the gauge field, the problem is reduced to that concerning a free Fermi gas. Two types of antiferromagnetic ordering (the Néel and collinear ones) are considered. By calculating the ground-state energies, the phase transitions induced by the interaction frustration were analyzed. K e y w o r d s: two-dimensional quantum spin models, frustrated models, fermionization.

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“…The Cu spin subsystem is described by the S = 1 2 Heisenberg model at T = 0. For the value of the correlation functions we use the results of [9] where this model was treated in the framework of spherically symmetrical Green's functions theory. It is important that we take into account that bf S Q S Q is a macroscopic value and is equal to a square of effective sublattice magnetization:…”

mentioning

confidence: 99%

Redistribution of the hole spectral weight due to longrange spin correlations in the three-band Hubbard model

et al. 1997

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In the framework of the three-band model for CuO 2 plane in hightemperature superconductors the spectrum of the spin-polaron hole exitation is investigated. The problem is treated taking into account the coupling of a local polaron with the antiferromagnetic spin wave with Q = (π, π).This leads to the essential changes of the lowest polaron band ǫ 1 (k) and the strong redistribution of the bare electron filling. PACS number(s): 74.72.-h. 75.10-b In order to understand the nature of high-temperature superconductors it is important to describe properly the motion of a hole in the CuO 2 plane [1,2]. This motion takes place on the antiferromagnetic (AFM) spin background of copper spins and it must be treated as a correlated motion of a hole coupled to spin excitations (a spin polaron). Usually the spin polaron is studied within the frameworks of the t-J model [1] and the three-band Hubbard model [3,4,5]. In the previous works the spin polaron problem was studied mainly in the approximation of a small radius polaron ( an analogous of a Zang -Rise polaron). In the present work, for the first time, the long range order of the AFM background is taken into account by introducing an additional new spin polaron of an infinite radius -a bound state of a charge exitation and a spin wave with Q = (π, π).We shall show that the introduction of such a 1

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Checkerboard-spin liquid-stripe state continuous transition in a frustrated Heisenberg antiferromagnet on a square lattice

Cited by 38 publications

References 12 publications

Effect of frustrations on magnetism in the Ru double perovskiteSr2YRuO6

Effect of frustrations on magnetism in the Ru double perovskiteSr2YRuO6

Two-Dimensional Spin-1/2 J1 – J'1 – J2 Heisenberg Model within Jordan–Wigner Transformation

Redistribution of the hole spectral weight due to longrange spin correlations in the three-band Hubbard model

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