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arXiv:cond-mat/9604144 · Physical Review Letters

Dynamics of Coupled Quantum Spin Chains

Heinz J. Schulz

Published Sep 23, 1996• 340 citations
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Abstract

Static and dynamical properties of weakly coupled antiferromagnetic spin chains are treated using a mean-field approximation for the interchain coupling and exact results for the resulting effective one-dimensional problem. Results for staggered magnetization, N\'eel temperature, and spin wave excitations are in agreement with experiments on ${\mathrm{KCuF}}_{3}$. The existence of a narrow longitudinal mode is predicted. The results are in agreement with general scaling arguments, contrary to spin wave theory.

DOI
10.1103/physrevlett.77.2790

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Static and dynamical properties of weakly coupled antiferromagnetic spin chains are treated using a mean-field approximation for the interchain coupling and exact results for the resulting effective one-dimensional problem. Results for staggered magnetization, N'eel temperature, and spin wave excitations are in agreement with experiments on KCuF3{\mathrm{KCuF}}_{3}KCuF3​. The existence of a narrow longitudinal mode is predicted. The results are in agreement with general scaling arguments, contrary to spin wave theory.
Calculations of the thermodynamic quantities, and the spectra of spinons, triplet excitations, and two-particle spin-singlet (Δ S z = 0,±1) excitations for a weakly coupled antiferromagnetic S = 1/2 spin chain are made using a mean-field approximation for the interchain couplings ( J 2 ) by the quantum Monte Carlo method. The mass gaps in these excitation spectra are estimated as functions of the interchain coupling. The critical field H c , and the temperatures at which the spinon and singlet gaps close ( T 1 and T 2 , respectively) are obtained. Some peculiarities of the staggered magnetization, the specific heat, and the spin-spin correlation function are found at T 1 = 0.9 J 2 , T 2 = 1.5 J 2 , H c = 3.8 J 2 , as determined by linear function fitting for J 2 / J 1 <0.15. The intrachain and interchain couplings, and the staggered magnetization for KCuF 3 , Sr 2 CuO 3 , and Ca 2 CuO 3 are estimated, and mass gaps are predicted to exist in the spectra of the spinons and the singlet two-particle excitations.
Using large-scale determinant quantum Monte Carlo simulations in combination with the stochastic analytical continuation, we study two-particle dynamical correlation functions in the anisotropic square lattice of weakly coupled one-dimensional (1D) Hubbard chains at half filling and in the presence of weak frustration. The evolution of the static spin structure factor upon increasing the interchain coupling is suggestive of the transition from the power-law decay of spin-spin correlations in the 1D limit to long-range antiferromagnetic order in the quasi-1D regime and at T=0T=0T=0. In the numerically accessible regime of interchain couplings, the charge sector remains gapped. The low-energy momentum dependence of the spin excitations is well described by the linear spin-wave theory with the largest intensity located around the antiferromagnetic wave vector. This magnon mode corresponds to a bound state of two spinons. At higher energies the spinons deconfine and we observe signatures of the two-spinon continuum which progressively fade away as a function of interchain hopping.
The ordering of weakly coupled random antiferromagnetic S=1/2S=1/2S=1/2 chains, as relevant for the recent experimentally investigated spin chain materials, is considered theoretically. The one-dimensional isotropic Heisenberg model with random exchange interactions is treated numerically on finite chains with the density-matrix renormalization-group approach as well as with the standard renormalization analysis, both within the mean-field approximation for interchain coupling ${J}_{\ensuremath{\perp}}$. Results for the ordering temperature TN{T}_{N}TN​ and for the ordered moment m0{m}_{0}m0​ are presented and are both reduced with increasing disorder, agreeing with the experimental observations. The most pronounced effect of the random singlet concept appears to be a very large span of local ordered moments, becoming wider with decreasing ${J}_{\ensuremath{\perp}}$, consistent with the $\ensuremath{\mu}$-SR experimental findings.
Quasi-one-dimensional quantum antiferromagnets formed by a ddd-dimensional hypercubic lattice of weakly coupled spin- 12\frac{1}{2}21​ antiferromagnetic Heisenberg chains are studied by combining exact results in one-dimension and renormalization group analyses of the interchain correlations. It is shown that ddd-dimensional magnetic long-range order develops at zero temperature for infinitesimal antiferromagnetic or ferromagnetic interchain couplings. In the presence of weak bond alternations, the order-disorder transition occurs at a finite interchain coupling. Relevances to the lightly doped quantum antiferromagnets and multilayer quantum Hall systems are discussed.
We study weakly coupled S = 1/2 quantum Heisenberg antiferromagnetic chains in an effective staggered field. Applying mean-field (MF) theory, spin-wave theory and chain MF (CMF) theory, we can see analytically some effects of the staggered field in this higher dimensional spin system. In particular, when the staggered field and the inter-chain interaction compete with each other, we conjecture from the MF theory that a nontrivial phase is present. The spin wave theory predicts that the behavior of the gaps induced by a staggered field is different between the competitive case and the non-competitive case. When the inter-chain interactions are weak enough, we can improve the MF phase diagram by using CMF theory and the analytical results of field theories. The ordered phase region predicted by the CMF theory is fairly smaller than one of the MF theory. Cu-benzoate, CuCl2·2DMSO (dimethylsulphoxide), BaCu2(Si1-xGex)2O7, etc., could be described by our model in enough low temperature.
We study weakly coupled antiferromagnetic spin chains in their ordered phase by combining an exact solution of the single-chain problem with a random-phase-approximation analysis of the interchain interaction. A single chain is described by a quantum Sine-Gordon model and dynamical staggered susceptibilities are determined by employing the form-factor approach to quantum correlation functions. We consider both antiferromagnetic order encountered in quasi-one-dimensional materials such as KCuF3{\mathrm{KCuF}}_{3}KCuF3​ and spin-Peierls order as found in CuGeO3.{\mathrm{CuGeO}}_{3}.CuGeO3​.