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

Abstract

We apply the rotation-invariant Green's function method to study the finite-temperature properties of a $S=1/2$ sawtooth-chain (also called $\Delta$-chain) antiferromagnetic Heisenberg model at the fully frustrated point when the exchange couplings along the straight-line and zig-zag paths are equal. We also use 13 terms of high-temperature expansion series and interpolation methods to get thermodynamic quantities for this model. We check the obtained predictions for observable quantities by comparison with numerics for finite systems. Although our work refers to a one-dimensional case, the utilized methods work in higher dimensions too and are applicable for examining other frustrated quantum spin lattice systems at finite temperatures.

arXiv comment13 pages, 8 figures

References in corpus (57)

• Macroscopic magnetization jumps due to independent magnons in frustrated quantum spin lattices
• The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins
• Many-body Green's function theory of Heisenberg films
• Quantum $J_1$--$J_2$ antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering
• Disorder-Free Localization and Many-Body Quantum Scars from Magnetic Frustration
• Magnetism of the N=42 kagome lattice antiferromagnet
• Elementary excitations in the $\Delta$-chain
• On Quantum Solitons in the Sawtooth Lattice
• Specific heat and high-temperature series of lattice models: interpolation scheme and examples on quantum spin systems in one and two dimensions
• Tenth-order high-temperature expansion for the susceptibility and the specific heat of spin-s Heisenberg models with arbitrary exchange patterns: Application to pyrochlore and kagome magnets
• High field properties of geometrically frustrated magnets
• Quantum Magnetism in Minerals
• Eighth-order high-temperature expansion for general Heisenberg Hamiltonians
• Specific heat of the S=1/2 Heisenberg model on the kagome lattice: high-temperature series expansion analysis
• The "Square Kagome" Quantum Antiferromagnet and the Eight Vertex Model
• One-dimensional sawtooth and zigzag lattices for ultracold atoms
• Green's-function theory of the Heisenberg ferromagnet in a magnetic field
• The pyrochlore S=1/2 Heisenberg antiferromagnet at finite temperature
• Quantum Topological Excitations: from the Sawtooth Lattice to the Heisenberg Chain
• Possible inversion symmetry breaking in the $S=1/2$ pyrochlore Heisenberg magnet
• Accuracy of the finite-temperature Lanczos method compared to simple typicality-based estimates
• Frustrated magnetism and resonating valence bond physics in two-dimensional kagome-like magnets
• Thermodynamics of a one-dimensional frustrated spin-1/2 Heisenberg ferromagnet
• The spin-half Heisenberg antiferromagnet on two Archimedian lattices: From the bounce lattice to the maple-leaf lattice and beyond
• Green's function approach to the magnetic properties of the kagome antiferromagnet
• Pinwheel valence-bond-crystal ground state of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the $shuriken$ lattice
• Magnetization process of atacamite: a case of weakly coupled $S=1/2$ sawtooth chains
• Spin susceptibility of quantum magnets from high to low temperatures
• Effect of perturbations on the kagome $S=1/2$ antiferromagnet at all temperatures
• Thermodynamics of low dimensional spin-1/2 Heisenberg ferromagnets in an external magnetic field within Green function formalism
• Topological Nematic Spin Liquid on the Square-Kagome Lattice
• Another Exact Ground State of a 2D Quantum Antiferromagnet
• Thermodynamics of the spin-half square-kagome lattice antiferromagnet
• Adapting Planck's route to investigate the thermodynamics of the spin-half pyrochlore Heisenberg antiferromagnet
• Quantum Monte Carlo simulations in the trimer basis: first-order transitions and thermal critical points in frustrated trilayer magnets
• Interpolation between low and high temperatures of the specific heat for spin systems
• Flat band, spin-1 Dirac cone, and Hofstadter diagram in the fermionic square kagome model
• Finite-temperature properties of the extended Heisenberg model on a triangular lattice
• Thermodynamics of the pyrochlore-lattice quantum Heisenberg antiferromagnet
• Metamagnetic jump in the spin-1/2 antiferromagnetic Heisenberg model on the square-kagome lattice
• Enhancement of magnetization plateaus in low dimensional spin systems
• Quantum antiferromagnet bluebellite comprising a maple-leaf lattice made of spin-1/2 Cu${}^{2+}$ ions
• Flat-band spin dynamics and phonon anomalies of the saw-tooth spin-chain system Fe${}_2$O(SeO${}_3$)${}_2$
• Variety of order-by-disorder phases in the asymmetric $J_1-J_2$ zigzag ladder: From the delta chain to the $J_1-J_2$ chain
• Analytical and numerical studies of the one-dimensional sawtooth chain
• Ferrimagnetism in delta chain with anisotropic ferromagnetic and antiferromagnetic interactions
• Ground-state and thermodynamic properties of the spin-$\frac{1}{2}$ Heisenberg model on the anisotropic triangular lattice
• Thermodynamics of the kagome-lattice Heisenberg antiferromagnet with arbitrary spin $S$
• Thermodynamics of the pyrochlore Heisenberg ferromagnet with arbitrary spin $S$
• Dimensional reduction in quantum spin-1/2 system on a 1/7-depleted triangular lattice
• Melting of magnetization plateaus for kagome and square-kagome lattice antiferromagnets
• Quantum spin spiral ground state of the ferrimagnetic sawtooth chain
• Anomalous thermodynamics of a quantum spin system with large residual entropy
• Spectral characteristics of the antiferromagnetic spin-1/2 Heisenberg model on the square lattice in a magnetic field
• The spin-$\frac{1}{2}$ Heisenberg ferromagnet on the pyrochlore lattice: A Green's function study
• Quantum Heisenberg model on a sawtooth-chain lattice: Rotation-invariant Green's function method
• Antikink dispersions of the $J_1$-$J_2$ sawtooth spin-1/2 anisotropic Heisenberg antiferromagnetic chain

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