Calculation of the singlet-triplet gap of the antiferromagnetic Heisenberg model on a ladder

Azzouz, Mohamed; Chen, Liang; Moukouri, S.

doi:10.1103/physrevb.50.6233

Cited by 63 publications

(59 citation statements)

References 10 publications

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“…The simple replacement by a flux phase shows only poor agreement with the DMRG result. It is interesting to note, however, that the spin gap remains finite for all J ⊥ /J > 0 within the π-flux treatment of the phase factor, as has been observed by Azzouz et al 21 The mean field evaluation of the phase factor (thin solid line) improves the form of the dispersion at least qualitatively. For a reasonable quantitative agreement with the exact dispersion, however, it seems to be necessary to consider also the correlations related to the phase factor (thick solid line).…”

Section: Appendix C: Role Of the Phase Factorsupporting

confidence: 61%

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Jordan-Wigner approach to dynamic correlations in spin ladders

Nunner

Kopp

2004

Phys. Rev. B

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We present a method for studying the excitations of low-dimensional quantum spin systems based on the Jordan-Wigner transformation. Using an extended RPA-scheme we calculate the correlation function of neighboring spin flips which well approximates the optical conductivity of Sr2CuO3. We extend this approach to the two-leg S = 1 2 -ladder by numbering the spin operators in a meander-like sequence. We obtain good agreement with the optical conductivity of the spin ladder compound (La,Ca)14Cu24O41 for polarization along the rungs. For polarization along the legs higher order correlations are important to explain the weight of high-energy continuum excitations and we estimate the contribution of 4-and 6-fermion processes.

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Section: Appendix C: Role Of the Phase Factorsupporting

confidence: 61%

“…There are no phase factors in the product of two spin operators on the same rung because they are neighboring along the meander path. Therefore the only 4-fermion process results from the Ising-like term in the rung operator (21).…”

Section: 17mentioning

confidence: 99%

Jordan-Wigner approach to dynamic correlations in spin ladders

Nunner

Kopp

2004

Phys. Rev. B

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“…Similar results were obtained by White, Noack and Scalapino (1994). In addition, a spin-gap appears in the one-band Hubbard model at half-filling if defined on a two-leg ladder (see Noack, White and Scalapino, 1994;Azzouz, Chen and Moukouri, 1994). This result is reasonable since the Heisenberg model is recovered from the strong-coupling U/t limit of the one-band Hubbard model.…”

Section: Undoped Spin Ladder Modelsmentioning

confidence: 99%

Experiments on ladders reveal a complex interplay between a spin-gapped normal state and superconductivity

1999

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In recent years, the study of ladder materials has developed into a well-established area of research within the general context of strongly correlated electrons. This effort has been triggered by an unusual cross-fertilization between theory and experiments. In this paper, the main experimental results obtained in the context of ladders are reviewed from the perspective of a theorist. Emphasis is given to the many similarities between the two-dimensional high-T c cuprates and the two-leg ladder compounds, including Sr 14−x Ca x Cu 24 O 41 ([14-24-41]) which has a superconducting phase at high pressure and a small hole density. Examples of these similarities include regimes of linear resistivity versus temperature in metallic ladders and a normal state with spin gap or pseudogap characteristics. It is remarked that the ladder [14-24-41] is the first superconducting Cu oxide material with a non-square-lattice layered arrangement, and certainly much can be learned from a careful analysis of this compound. A short summary of the main theoretical developments in this field is also included, as well as a brief description of the properties of non-Cu-oxide ladders. Suggestions by the author on possible experiments are described in the text. Overall, it is concluded that the enormous experimental effort carried out on ladders has already unveiled quite challenging and interesting physics that adds to the rich behaviour of electrons in transition metal-oxides, and in addition contributes to the understanding of the two-dimensional cuprates. However, considerable work still needs to be carried out to fully understand the interplay between charge and spin degrees of freedom in these materials.

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“…Applications to spin chains with high spin [8,9], dimerization and/or frustration [10][11][12][13][14][15], together with extensions to coupled spin chains [16], models with itinerant fermions [17,18], Kondo systems [19][20][21][22], as well as coupled fermion chains [23] have followed, even in cases of intermediate doping. Formulations for systems with single [24] as well as randomly distributed [25] impurities and disorder [26] have also been forthcoming.…”

Section: The Dmrg Methodsmentioning

confidence: 99%

“…Also, Pati et al [15] appear to have discovered such a point in the S = 1 case of (12) at J2 = 0.730 ± 0.05. Ladder models consisting of two coupled Heisenberg chains have been studied [16]. The phase transition whereby a gap opens on the introduction of interchain exchange, has been characterised.…”

Section: Direct Calculations Of δ or ξmentioning

confidence: 99%

Applications of Density Matrix Renormalization Group to Problems in Magnetism

1997

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The application of real space renormalization group methods to quantum lattice models has become a topic of great interest following the development of the density matrix renormalization group by White. This method has been used to find the ground and low-lying excited state energies and wave functions of quantum spin models in which the form of the ground state is not clear, for instance because the interactions are frustrated. It has also been applied to fermion problems where the tendency for localization due to the strong Coulomb repulsion is opposed by the lowering of the kinetic energy which occurs as a result of electron transfer. The approach is particularly suitable for one-, or quasi-one-dimensional problems. The method involves truncating the Hilbert space in a systematic and optimised manner. Results for the ground state energy are thus variational bounds. The results for low-lying energies and correlation functions for one-dimensional systems have unprecedented accuracy and the method has become the method of choice for solving one-dimensional quantum spin problems. We review the method and results obtained for the spin-1 chain with biquadratic exchange as well as the spin-1/2 model with competing nearest and next nearest neighbour exchange will be described. More recently, the density matrix renormalization group has been applied to reformulate the coupling constant renormalization group approach which is appropriate for the study of critical properties. This approach has been applied to the anisotropic spin-1/2 Heisenberg chain. Finally, we discuss recent work which has borne promising applications in two dimensions -the Ising model and the two-dimensional Hubbard model.

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Calculation of the singlet-triplet gap of the antiferromagnetic Heisenberg model on a ladder

Cited by 63 publications

References 10 publications

Jordan-Wigner approach to dynamic correlations in spin ladders

Jordan-Wigner approach to dynamic correlations in spin ladders

Experiments on ladders reveal a complex interplay between a spin-gapped normal state and superconductivity

Applications of Density Matrix Renormalization Group to Problems in Magnetism

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