Correlation functions in one-dimensional spin lattices with Ising and Heisenberg bonds

Abstract

A general technique of exact calculation of any correlation functions for the special class of one-dimensional spin models containing small clusters of quantum spins assembled to a chain by alternating with the single Ising spins is proposed. The technique is a natural generalization of that in the models solved by a classical transfer matrix. The general expressions for corresponding matrix operators which are the key components of the technique are obtained. As it is clear from the general principles, the decay of the correlation functions of various types is explicitly shown to be governed by a single correlation length. The technique is illustrated by two examples: symmetric diamond chain and asymmetric sawtooth chain.

12 pages, 5 figures

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Cited by in corpus (18)

• Magnetization plateaus of an exactly solvable spin-1 Ising-Heisenberg diamond chain
• Magnetization non-rational quasi-plateau and spatially modulated spin order in the model of the single-chain magnet, [{(CuL)_2 Dy}{Mo(CN)_8}] 2CH_3CN H_2O
• Correlation functions for a spin-$\frac{1}{2}$ Ising-XYZ diamond chain: Further evidence for quasi-phases and pseudo-transitions
• Spin frustration and fermionic entanglement in an exactly solved hybrid diamond chain with the localized Ising spins and mobile electrons
• On the absence of actual plateaus in zero-temperature magnetization curves of quantum spin clusters and chains
• Exact results for a generalized spin-1/2 Ising-Heisenberg diamond chain with the second-neighbor interaction between nodal spins
• Thermodynamic curvature for a two-parameter spin model with frustration
• Exactly solved mixed spin-(1,1/2) Ising-Heisenberg distorted diamond chain
• Non-conserved magnetization operator and `fire-and-ice' ground states in the Ising-Heisenberg diamond chain
• 1D Spin-Crossover Molecular Chain with Degenerate States
• Magnetization plateaus and enhanced magnetocaloric effect of a spin-1/2 Ising-Heisenberg and Heisenberg double sawtooth ladder with four-spin interaction
• Exactly solvable spin-1 Ising-Heisenberg diamond chain with the second-neighbor interaction between nodal spins
• Quantum entanglement in mixed-spin trimer: Effects of a magnetic field and heterogeneous g-factors
• Enhanced magnetocaloric effect in a mixed spin-(1/2, 1) Ising-Heisenberg two-leg ladder with strong-rung interaction
• Effect of compression in molecular spin-crossover chains
• Ergodic and non-ergodic many-body dynamics in strongly nonlinear lattices
• On flat bands in the $J_1$-$J_2$-$J_3$ XXZ sawtooth chain
• Spin-1/2 Ising-Heisenberg distorted diamond chain with antiferromagnetic Ising and ferromagnetic Heisenberg interactions