Thermodynamics of spin-12tetrameric Heisenberg antiferromagnetic chain

Abstract

The thermodynamic properties of a spin $S=1/2$ tetrameric Heisenberg antiferromagnetic chain with alternating interactions ${\text{AF}}_{1}{\text{-AF}}_{2}{\text{-AF}}_{1}\text{-F}$ (AF and F denote the antiferromagnetic and ferromagnetic couplings, respectively) are studied by means of the transfer-matrix renormalization-group method and Jordan-Wigner transformation. It is found that in the absence of magnetic field, the thermodynamic behaviors are closely related to the gapped low-lying excitations, and a novel structure with three peaks in the temperature dependence of specific heat is unveiled. In a magnetic field, a phase diagram in the temperature-field plane for the couplings satisfying ${J}_{{\text{AF}}_{1}}={J}_{{\text{AF}}_{2}}={J}_{\text{F}}$ is obtained, in which various phases are identified. The temperature dependence of thermodynamic quantities including the magnetization, susceptibility, and specific heat are studied to characterize the corresponding phases. It is disclosed that the magnetization has a crossover behavior at low temperature in the Luttinger liquid phase, which is shown falling into the same class as that in the $S=1$ Haldane chain. In the plateau regime, the thermodynamic behaviors alter at a certain field, which results from the crossing of two excitation spectra. By means of the fermion mapping, it is uncovered that the system has four spectra from fermion and hole excitations that are responsible for the observed thermodynamic behaviors.