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arXiv:cond-mat/9507083 · Physical review. B, Condensed matter

Random-exchange quantum Heisenberg chains

Akira Furusaki, Manfred Sigrist, E. Westerberg, Patrick A. Lee, Katsuhiro Tanaka, Naoto Nagaosa

Published Dec 1, 1995• 18 citations
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Abstract

The one-dimensional quantum Heisenberg model with random \ifmmode\pm\else\textpm\fi{}J bonds is studied for S=1/2 and S=1. The specific heat and the zero-field susceptibility are calculated by using high-temperature series expansions and the quantum transfer matrix method. The susceptibility shows a Curie-like temperature dependence at low temperatures as well as at high temperatures. The numerical results for the specific heat suggest that there are anomalously many low-lying excitations. The qualitative nature of these excitations is discussed based on the exact diagonalization of finite-size systems.

DOI
10.1103/physrevb.52.15930

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The one-dimensional quantum Heisenberg model with random \ifmmode\pm\else\textpm\fi{}J bonds is studied for S=1/2 and S=1. The specific heat and the zero-field susceptibility are calculated by using high-temperature series expansions and the quantum transfer matrix method. The susceptibility shows a Curie-like temperature dependence at low temperatures as well as at high temperatures. The numerical results for the specific heat suggest that there are anomalously many low-lying excitations. The qualitative nature of these excitations is discussed based on the exact diagonalization of finite-size systems.
The Heisenberg chain with random $\ifmmode\pm\else\textpm\fi{}J$ bonds is studied for the quantum spin s=12s=\frac{1}{2}s=21​ and in the classical limit. The former is treated by high-temperature expansion and transfer matrix calculation while the latter can be analyzed exactly. The disorder leads to a 1T\frac{1}{T}T1​ behavior of the low-temperature susceptibility in the classical system. For s=12s=\frac{1}{2}s=21​ our analysis reveals a significant residual entropy at low temperature. From this we conclude that for quantum spins the susceptibility exhibits three different regimes in temperature and that the specific heat has a peak in the very low-temperature regime.
The quantum transfer-matrix method (QTM) has been applied to study the finite-temperature static properties of the spin S=1S=1S=1 antiferromagnetic Heisenberg chains in a wide range of the single-ion anisotropy and temperatures. The high-resolution QTM simulation data are obtained for the zero-field susceptibility, specific heat, as well as for the field-dependent magnetization. The microscopic parameters of a number of real quasi-one-dimensional compounds are found from fitting procedures, some theoretical approaches are numerically verified and low-temperature extensions of high-temperature series are given in terms of Chebyshev polynomials.
Thermodynamic properties of the quantum Heisenberg spin chains with S=1/2,S=1/2,S=1/2, 1, and 3/23/23/2 are investigated using the transfer-matrix renormalization-group method. The temperature dependence of the magnetization, susceptibility, specific heat, spin-spin correlation length, and several other physical quantities in a zero or finite applied field are calculated and compared. Our data agree well with the Bethe ansatz, exact diagonalization, and quantum Monte Carlo results and provide further insight into the quantum effects in the antiferromagnetic Heisenberg spin chains.
One-dimensional Heisenberg spin 1/2 chains with random ferro- and antiferromagnetic bonds are realized in systems such as Sr3CuPt1−xIrxO6Sr_3 CuPt_{1-x} Ir_x O_6Sr3​CuPt1−x​Irx​O6​. We have investigated numerically the thermodynamic properties of a generic random bond model and of a realistic model of Sr3CuPt1−xIrxO6Sr_3 CuPt_{1-x} Ir_x O_6Sr3​CuPt1−x​Irx​O6​ by the quantum Monte Carlo loop algorithm. For the first time we demonstrate the separation into three different temperature regimes for the original Hamiltonian based on an exact treatment, especially we show that the intermediate temperature regime is well-defined and observable in both the specific heat and the magnetic susceptibility. The crossover between the regimes is indicated by peaks in the specific heat. The uniform magnetic susceptibility shows Curie-like behavior in the high-, intermediate- and low-temperature regime, with different values of the Curie constant in each regime. We show that these regimes are overlapping in the realistic model and give numerical data for the analysis of experimental tests.
The quantum transfer-matrix method was applied to study the finite--temperature static properties of the spin S = 1 antiferromagnetic Heisen- berg chains in a wide range of the single-ion anisotropy and temperatures.The high-resolution quantum transfer-matrix simulation data are obtained for the zero-field susceptibility, specific heat as well as for the field-dependent magnetization.The microscopic parameters of a number of real quasi-one--dimensional compounds are found from fitting procedures, some theoretical approaches are numerically verified and an extension of the technique to a non-uniform bond alternating molecular magnets is ałso put forward.