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Journal of Physics A Mathematical and General

Low-temperature properties of the generalized two-chain quantum spin model

Sooa Park, K Lee

Published Aug 7, 1998• 7 citations
Publisher

Abstract

We consider an exactly solvable two-chain quantum spin- model in a generalized form with enhanced spin frustration. This model is exactly diagonalized via Bethe's ansatz. The low-temperature specific heat of the system is obtained with and without a magnetic field, using the thermodynamic Bethe ansatz equations. We also calculate the magnetic susceptibility in a sufficiently weak field, yielding typical logarithmic corrections. The spin frustration affects only the amplitudes in the magnetic susceptibility and the specific heat. This extends the previous results for a simple two-chain quantum spin model to the generalized one.

DOI
10.1088/0305-4470/31/31/004

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We consider an exactly solvable two-chain quantum spin- model in a generalized form with enhanced spin frustration. This model is exactly diagonalized via Bethe's ansatz. The low-temperature specific heat of the system is obtained with and without a magnetic field, using the thermodynamic Bethe ansatz equations. We also calculate the magnetic susceptibility in a sufficiently weak field, yielding typical logarithmic corrections. The spin frustration affects only the amplitudes in the magnetic susceptibility and the specific heat. This extends the previous results for a simple two-chain quantum spin model to the generalized one.
We have extracted the leading low-temperature contributions to the specific heat and the magnetic susceptibility from the thermodynamic Bethe-ansatz equations of the SU(2) invariant ferromagnetic Heisenberg chain of arbitrary spin S. This extends previous analytic results for S=1/2 to other spin values. The critical exponent for the specific heat is \ensuremath{\alpha}=-1/2, that for the susceptibility is \ensuremath{\gamma}=2, and that for the correlation length is \ensuremath{\nu}=1. The susceptibility and the correlation length exhibit logarithmic corrections, reflecting the analogy to the Kondo problem. These logarithmic corrections are quenched by relatively small magnetic fields. In large fields the energy required to flip a spin gives rise to an exponential activation.
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.
We have extracted the leading low-temperature contributions to the specific heat and the magnetic susceptibility from the thermodynamic Bethe-Ansatz equations of the SU(3) invariant ferromagnetic Heisenberg chain of spin 1. The critical exponents for the specific heat, the susceptibility, and the correlation length are $\ensuremath{\alpha}=\ensuremath{-}\frac{1}{2}$, $\ensuremath{\gamma}=2$, and $\ensuremath{\nu}=1$, respectively. The susceptibility and the correlation length exhibit logarithmic corrections, which are quenched by relatively small magnetic fields. In large fields, the energy required to flip a spin gives rise to an exponential activation.
We present a new application of the traditional thermodynamic Bethe ansatz to the spin-1/2 antiferromagnetic uniform Heisenberg chain and derive exact nonlinear integral equations for just two functions describing the elementary excitations. By using this approach, the magnetic susceptibility chi and specific heat C versus temperature T are calculated to high accuracy for 5x10(-25)</=T/J</=5. The chi(T) data agree very well at low T with the asymptotically exact theoretical low- T prediction of Lukyanov [Nucl. Phys. B522, 533 (1998)]. The unknown coefficients of the second and third lowest-order logarithmic correction terms in Lukyanov's theory for C(T) are estimated from the C(T) data.