Hutak T. Thermodynamics of frustrated quantum spin systems

The thesis is devoted to the study of the thermodynamics of the frustrated quantum spin systems. To reveal the reason for the emergence of pseudo-transitions, we consider a number of decorated one-dimensional systems. Namely, the two-leg ladder Ising model with trimer rungs, the spin–1/2 Ising–XYZ diamond chain, the double–tetrahedral chain of localized Ising spins and mobile electrons, and the spin–1/2 Ising–Heisenberg double-tetrahedral chain. After a decoration-iteration transformation, the effective Hamiltonian for the two-leg ladder Ising model with trimer rungs becomes the simple two-leg rail-road Ising ladder Hamiltonian with the temperature-dependent interactions for the interleg coupling. At some finite temperature (pseudocritical temperature) vanishes. Effectively, this corresponds to a splitting of the two-leg ladder into two independent Ising chains. For sufficiently small values of the pseudocritical temperature (in the units of exchange coupling of the chain), the traces of the simple Ising chain criticality at zero temperature and zero field are clearly seen. Around the pseudocritical temperature (but not in the immediate vicinity of the pseudocritical temperature) the model shows pseudo-critical behavior. The decoration-iteration transformation for a number of considered decorated classical–quantum chains leads to the simple Ising chain Hamiltonian with the temperature-dependent exchange interaction and magnetic field. The effective magnetic field vanishes at the pseudocritical temperature and, consequently, the model corresponds to the simple Ising chain at zero magnetic field. Therefore, the low-temperature peculiarities of the decorated Ising chains show up from the simple Ising chain criticality at the zero temperature and field. Quasicritical exponents of the decorated classical–quantum chains coincide with the ones obtained for the two-leg Ising ladder. As a result, the reason for the peculiar low-temperature behavior of some spin–1/2 decorated (frustrated) one-dimensional Ising models has been revealed. To study the influence of geometrical frustration on thermodynamics of a three-dimensional quantum spin systems we consider a pyrochlore lattice. The pyrochlore lattice is the most frustrated lattice in three dimensions. Thermodynamic and dynamic properties of quantum S=1/2 ferromagnetic Heisenberg model were studied by the double-time temperature-dependent Green functions method within the random phase approximation. The value of the critical temperature and the temperature dependence of the magnetization in the ferromagnetic phase and the magnetic susceptibility in the paramagnetic phase were found from the analysis of the self-consistent equation for magnetization. We compare the magnetization and the specific heat (for the temperatures below the critical one) and the magnetic susceptibility (for the temperatures above the critical one) with the results of quantum Monte Carlo simulations. The dynamic structure factor was compared with inelastic neutron scattering data for Lu2V2O7 material and a satisfactory agreement has been found. To study the thermodynamics of the quantum S=1/2 antiferromagnetic Heisenberg model we used the entropy method. The interpolation between high temperatures (based on the 13-th order high-temperature expansion for the specific heat and the magnetic susceptibility) and low temperatures according to different scenarios for the low-energy excitation spectrum has been made. The low-temperature dependence of the specific heat is determined by the nature of low-energy excitation spectrum of the system. In the case of gapless spectrum, the specific heat follows a power-law behavior, whereas for the gapped spectrum, the specific heat is thermally activated. The interpolation within the framework of the entropy method was made for both cases. We apply a self-consistent procedure within the entropy method based on the largest number of coinciding Pade approximants to analyze the thermodynamic observables. For the available order of the high-temperature expansion, the assumption of the gapless spectrum is more robust. The specific heat does not have any extra low-temperature features like a peak or shoulder. However, the location of the main maximum is significantly shifted to lower temperatures. This behavior is independent of the assumed type of low-energy excitations. The magnetic susceptibility has a broad maximum.