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Spin-half Heisenberg antiferromagnet on a symmetric sawtooth chain: rotation-invariant Green’s functions and high-temperature series

Taras Hutak, Taras Krokhmalskii, Oleg Derzhko +1 more

arXiv:2304.09682The European Physical Journal BApr 1, 20239 citations

Lattice distortions in a sawtooth chain with Heisenberg and Ising bonds

Stefano Bellucci A, Vadim Ohanyan

arXiv:0908.3594The European Physical Journal BMay 8, 201026 citations

Quantum topological excitations: from the sawtooth lattice to the Heisenberg chain

Steven A. Blundell, M. D. Núñez-Regueiro

arXiv:cond-mat/0204405The European Physical Journal BFeb 1, 200366 citations

Rotationally invariant approximation for the two-dimensional t−J model

A. Sherman, Michael Schreiber

Using the description in terms of the Hubbard operators hole and spin Green's functions of the two-dimensional $t\ensuremath{-}J$ model are calculated in an approximation that retains the rotation symmetry of the spin susceptibility in the paramagnetic state and has no predefined magnetic ordering. In this approximation, Green's functions are represented by continued fractions that are interrupted with the help of the decoupling corrected by the constraint of zero site magnetization in the paramagnetic state. Results obtained in this approach for an undoped $32\ifmmode\times\else\texttimes\fi{}32$ lattice (the Heisenberg model) and for one hole in a $4\ifmmode\times\else\texttimes\fi{}4$ lattice are in good agreement with Monte Carlo and exact-diagonalization data, respectively. In the limit of heavy doping the hole spectrum described by the obtained formulas acquires features of the spectrum of weakly correlated excitations.Using the description in terms of the Hubbard operators hole and spin Green's functions of the two-dimensional $t\ensuremath{-}J$ model are calculated in an approximation that retains the rotation symmetry of the spin susceptibility in the paramagnetic state and has no predefined magnetic ordering. In this approximation, Green's functions are represented by continued fractions that are interrupted with the help of the decoupling corrected by the constraint of zero site magnetization in the paramagnetic state. Results obtained in this approach for an undoped $32\ifmmode\times\else\texttimes\fi{}32$ lattice (the Heisenberg model) and for one hole in a $4\ifmmode\times\else\texttimes\fi{}4$ lattice are in good agreement with Monte Carlo and exact-diagonalization data, respectively. In the limit of heavy doping the hole spectrum described by the obtained formulas acquires features of the spectrum of weakly correlated excitations.

arXiv:cond-mat/0201526Physical review. B, Condensed matterMar 26, 200231 citations

Green functions of the anisotropic Heisenberg model

J. Ginibre, C. Gruber

Communications in Mathematical PhysicsSep 1, 196915 citations

Magnetic order-disorder transition in the two-dimensional spatially anisotropic Heisenberg model at zero temperature

Dieter Ihle, C. Schindelin, Alexander Weiße +1 more

The ground-state properties of the spin-1/2 antiferromagnetic Heisenberg model with spatially anisotropic couplings on a square lattice are investigated by a spin-rotation-invariant Green's-function approach and by Lanczos diagonalizations on lattices up to 36 sites supplemented by finite-size scaling. We focus on the anisotropy-driven transition from the N\'eel state to a paramagnetic state with antiferromagnetic short-range order and on the spatial dependence of spin correlation functions. Our principal result is that a rather sharp crossover in the magnetic behavior occurs at the coupling ratio ${R}_{0}\ensuremath{\simeq}0.2 {(R=J}_{y}{/J}_{x}).$The ground-state properties of the spin-1/2 antiferromagnetic Heisenberg model with spatially anisotropic couplings on a square lattice are investigated by a spin-rotation-invariant Green's-function approach and by Lanczos diagonalizations on lattices up to 36 sites supplemented by finite-size scaling. We focus on the anisotropy-driven transition from the N\'eel state to a paramagnetic state with antiferromagnetic short-range order and on the spatial dependence of spin correlation functions. Our principal result is that a rather sharp crossover in the magnetic behavior occurs at the coupling ratio ${R}_{0}\ensuremath{\simeq}0.2 {(R=J}_{y}{/J}_{x}).$

arXiv:cond-mat/9904005Physical review. B, Condensed matterOct 1, 199927 citations

Quantum Heisenberg model on a sawtooth-chain lattice: rotation-invariant Green’s function method

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