This is a theoretical study of quantum stationary states and thermodynamics of two exactly solvable quantum models: a finite XX-chain with an “offshoot” that is connected via ZZ-interaction (Ising) to one of the chain nodes, and two different finite XX-chains joined through an additional ZZ-spin. It is shown that the spectrum can have impurity levels localized near the impurity spin, and the conditions for their manifestation are determined. The field and temperature dependences of the main thermodynamic characteristics of the models are investigated.
We present the results of our analytical and numerical study of quantum stationary states and the thermodynamics of exactly solvable finite linear spin-1/2 XX chain with one or two distorted links. The exact dispersion equations for the stationary states with one inverted spin for both cases have been derived. The corresponding spectrum consists of one quasi-continuous band and some localized impurity levels. The analytical inequalities for the values of the critical model parameters describing the appearance of local energy impurity levels above and below quasi-continuous band are obtained and analyzed. The field and the temperature dependences of the main thermodynamic characteristics of these models are studied. It is shown, that the appearance of the localized levels near the distorted links may effect significantly on the thermodynamic properties at low temperatures, leading to the additional singularities in the field and the temperature dependences of the principal thermodynamic characteristics. For example, the field dependence of z-projection of average total spin and the field dependence of the magnetization at zero temperature have the finite jumps associated with the quasi-continuous spectrum, and the impurity levels. The remnants of these jumps at rather low temperature are clearly visible. The average z-projections of the spins of distorted link(s) may decrease with the increasing of the magnetic field for some values of model parameters. The temperature dependence of the specific heat may demonstrate additional maxima at very low temperatures. The complex oscillatory pattern of the time dependence of the dynamical longitudinal pair correlation function and the autocorrelation function is associated with the finiteness of the models and the appearance of associated localized energy levels.
We consider an exactly solvable version of the quantum spin-1/2 orthogonal-dimer chain with the Heisenberg intra-dimer and Ising inter-dimer couplings.The investigated quantum spin system exhibits at zero temperature fractional plateaux at 1/4 and 1/2 of the saturation magnetization and it has a highly degenerate ground state at critical elds where the magnetization jumps.We study the eld dependence of the specic heat at low temperature.The lattice-gas description is formulated in a vicinity of critical elds to explain the low-temperature behaviour of specic heat.
We present an exact analytical solution for the one-dimensional Ising model in the presence of an external magnetic field applied periodically to every
k-th site. The problem is handled using the symmetrized transfer matrix approach, we derive a compact closed-form expression for the system's eigenvalues for arbitrary period
k. From the resulting free energy, we obtain exact expressions for the magnetization and zero-field susceptibility. Explicit results are presented for
k=1,
k=2, and
k=3 which is considered a novel result. We further analyze the spin-spin correlation functions, deriving the correlation length and the set of position-dependent correlation strength prefactors,
Aij. The framework highlights how impurity spacing suppresses thermodynamic responses, with susceptibility scaling as
χ∼β/k for large
k, offering insights into diluted magnetic systems and serving as a benchmark for quasiperiodic modulations. The correlation strengths exhibit a strong anisotropy, revealing a complex, non-local structure of spin fluctuations. These results provide a complete and rigorous benchmark for understanding the effects of periodic modulation in 1D systems.
Thermodynamic properties of the quantum Heisenberg spin chains with
S=1/2, 1, and
3/2 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.