Cumulant approach to weakly doped antiferromagnets

Vojta, Matthias; Becker, K. W.

doi:10.1103/physrevb.54.15483

Cited by 16 publications

(39 citation statements)

References 31 publications

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“…This result agrees with that found by the cumulant approach of Ref. [33], where our δ c values are somewhat lower (e. In Fig. 3 the uniform static spin susceptibility χ = (1/2) lim q→0 χ q at J/t = 0.3 is plotted as a function of doping at various temperatures.…”

Section: A Static Propertiessupporting

confidence: 91%

Dynamic spin susceptibility in thet−Jmodel

2009

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A relaxation-function theory for the dynamic spin susceptibility in the t-J model is presented. By a sum-rule-conserving generalized mean-field approximation (GMFA), the two-spin correlation functions of arbitrary range, the staggered magnetization, the uniform static susceptibility, and the antiferromagnetic correlation length are calculated in a wide region of hole doping and temperaturs. A good agreement with available exact diagonalization (ED) data is found. The correlation length is in reasonable agreement with neutron-scattering experiments on La 2−δ Sr δ CuO4. Going beyond the GMFA, the self-energy is calculated in the mode-coupling approximation. The spin dynamics at arbitrary frequencies and wave vectors is studied for various temperatures and hole doping. At low doping a spin-wave-type behavior is found as in the Heisenberg model, while at higher doping a strong damping caused by hole hopping occurs, and a relaxation-type spin dynamics is observed in agreement with the ED results. The local spin susceptibility and its ω/T scaling behavior are calculated in a reasonable agreement with experimental and ED data.

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Section: A Static Propertiessupporting

confidence: 91%

Dynamic spin susceptibility in thet−Jmodel

2009

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“…For instance, if we include two additional operators S n with three and four fluctuations on adjacent sites into the operator Ω (13) the transition point shifts to (J ⊥ /J ) c ∼ 2.9. However, the analytical and numerical effort to set-up and solve the non-linear equations equivalent to (12,14) increases drastically with including higher-order fluctuations.…”

Section: Ground-state Propertiesmentioning

confidence: 99%

Doped bilayer antiferromagnets: Hole dynamics on both sides of a magnetic ordering transition

Vojta

Becker

1999

Phys. Rev. B

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The two-layer square lattice quantum antiferromagnet with spins 1 2 shows a magnetic orderdisorder transition at a critical ratio of the interplane to intraplane couplings. We investigate the dynamics of a single hole in a bilayer antiferromagnet described by a t−J Hamiltonian. To model the spin background we propose a ground-state wave function for the undoped system which covers both magnetic phases and includes transverse as well as longitudinal spin fluctuations. The photoemission spectrum is calculated using the spin-polaron picture for the whole range of the ratio of the magnetic couplings. This allows for the study of the hole dynamics of both sides of the magnetic order-disorder transition. For small interplane coupling we find a quasiparticle with properties known from the single-layer antiferromagnet, e.g., the dispersion minimum is at (±π/2, ±π/2). For large interplane coupling the hole dispersion is similar to that of a free fermion (with reduced bandwidth). The cross-over between these two scenarios occurs inside the antiferromagnetic phase which indicates that the hole dynamics is governed by the local environment of the hole.

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“…For this reason it has previously been used to study strongly correlated electronic systems. [6][7][8] The introduction of cumulants ensures that expressions of physical quantities are always ''size consistent.'' For example, this implies that expectation values of extensive variables scale proportionally to the system size.…”

Section: Cumulant Approachmentioning

confidence: 99%

Construction of size-consistent effective Hamiltonians

Polatsek

Becker

1997

Phys. Rev. B

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For a system consisting of two interacting subsystems, effective Hamiltonians for one subsystem are usually constructed by integrating out the degrees of freedom of the second subsystem. In contrast to usual treatments, our method for deriving effective Hamiltonians is based on the introduction of cumulants. Cumulants guarantee size consistency, a property that is not always evident in other approaches. The formalism applies for any temperature. Our method is based on a matrix formulation in the framework of a recently introduced cumulantprojection method. This method allows the treatment of strongly correlated systems, where conventional diagrammatic techniques are difficult to apply. The relation with perturbation theory is also shown. As a simple application we discuss the small polaron problem. Evaluating the one-electron dispersion relation in the strong-coupling case shows good agreement with recent results from exact Lanczos diagonalization. Our method has substantial advantages over perturbation theory.

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Cumulant approach to weakly doped antiferromagnets

Cited by 16 publications

References 31 publications

Dynamic spin susceptibility in thet−Jmodel

Dynamic spin susceptibility in thet−Jmodel

Doped bilayer antiferromagnets: Hole dynamics on both sides of a magnetic ordering transition

Construction of size-consistent effective Hamiltonians

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