We study quantum spin models with nearest- and next-nearest-neighbor exchange interactions by means of exact solutions. Depending on the representation, the models can also be viewed as spin ladders with interchain couplings and with ring biquadratic spin-spin interactions. The ground-state phase diagram is constructed as a function of the next-nearest-neighbor couplings and an external magnetic field. Several quantum phase transitions in the ground state, including the possibility of a first-order quantum phase transition, governed by the external magnetic field, are predicted. The low-energy conformal behavior of the low-lying excitations is studied in the commensurate and incommensurate phases. Finally, the properties of the models at finite temperature are studied exactly. A finite set of nonlinear integral equations determining the thermodynamic potential at arbitrary temperature and external magnetic field is derived and solved in several important cases. The results for the magnetic susceptibility and the Sommerfeld coefficient of the specific heat are presented.
Advances in quantum computing technology have been made in recent years due to the evolution of spin clusters. Recent studies have tended towards spin cluster subgeometries to understand more complex structures better. These molecular magnets provide a multitude of phenomena via exchange interactions that allow for advancements in spintronics and other magnetic system applications due to the possibility of increasing speed, data storage, memory, and stability of quantum computing systems. Using the Heisenberg spin–spin exchange Hamiltonian and exact diagonalization, we examine the evolution of quantum energy levels and thermodynamic properties for various spin configurations and exchange interactions. The XXYY quantum spin tetramer considered in this study consists of two coupled dimers with exchange interactions α1J and α1′J and a dimer–dimer exchange interaction α2J. By varying spin values and interaction strengths, we determine the exact energy eigenstates that are used to determine closed-form analytic solutions for the heat capacity and magnetic susceptibility of the system and further analyze the evolution of the properties of the system based on the parameter values chosen. Furthermore, this study shows that the Schottky anomaly shifts towards zero as the ground-state of the system approaches a quantum phase transition between spin states. Additionally, we investigate the development of phase transitions produced by the convergence of the Schottky anomaly with both variable exchange interactions and external magnetic field.
In this study, we examine the thermodynamics and spin dynamics of spin-1/2 and spin-3/2 heptamers. Through an exact diagonalization of the isotropic Heisenberg Hamiltonian, we find the closed-form, analytical representations for thermodynamic properties, spin excitations, and neutron-scattering structure factors. Furthermore, we investigate the clusterlike excitations of quantum spin heptamer in the three-dimensional pyrochlore lattice material
MgCr2O4. Using a spin mapping of the spin-1/2 heptamer excitations, the calculated structure factors of the spin-3/2 heptamer are to be determined, which provides clarification for the spin excitations in
MgCr2O4. Overall, this study demonstrates the ability to use the spin mapping of structure factors for small spin systems to analyze more complex structures.
Accurate results are obtained for the low-temperature magnetization vs magnetic field of Heisenberg spin rings consisting of an even number
N of intrinsic spins
s=1∕2,1,3∕2,2,5∕2,3,7∕2 with nearest-neighbor antiferromagnetic exchange by employing a numerically exact quantum Monte Carlo method. A straightforward analysis of this data, in particular, the values of the level-crossing fields, provides accurate results for the lowest-energy eigenvalue
EN(S,s) for each value of the total spin quantum number
S. In particular, the results are substantially more accurate than those provided by the rotational band approximation. For $s\ensuremath{\leqslant}5∕2$, data are presented for all even $N\ensuremath{\leqslant}20$, which are particularly relevant for experiments on finite magnetic rings. Furthermore, we find that for $s\ensuremath{\geqslant}3∕2$, the dependence of
EN(S,s) on
s can be described by a scaling relation, and this relation is shown to hold well for ring sizes up to
N=80 for all intrinsic spins in the range $3∕2\ensuremath{\leqslant}s\ensuremath{\leqslant}7∕2$. Considering ring sizes in the interval $8\ensuremath{\leqslant}N\ensuremath{\leqslant}50$, we find that the energy gap between the ground state and the first excited state approaches zero proportional to $1∕{N}^{\ensuremath{\alpha}}$, where $\ensuremath{\alpha}\ensuremath{\approx}0.76$ for
s=3∕2 and $\ensuremath{\alpha}\ensuremath{\approx}0.84$ for
s=5∕2. Finally, we demonstrate the usefulness of our present results for
EN(S,s) by examining the
Fe12 ring-type magnetic molecule, leading to a more accurate estimate of the exchange constant for this system than has been obtained heretofore.
Several exactly solvable quantum spin models with incommensurate magnetic structures, which manifest quantum phase transitions between incommensurate and commensurate phases, are proposed. The ground-state and thermodynamic characteristics of these quantum spin antiferromagnetic models with the Dzyaloshinsky-Moriya antisymmetric exchange interaction and spin-frustrating next-nearest-neighbor, three-spin, and four-spin (ring exchange) interactions are exactly studied. We investigated the ground state phases of the considered models, as function of the magnetic anisotropy, Dzyaloshinsky-Moriya interaction, next-nearest-neighbor coupling constants, and external magnetic field. Several quantum phase transitions between magnetically incommensurate phases and between incommensurate and ferromagnetic phases are predicted, and the behavior of thermodynamic characteristics of those models at phase transitions is studied. We have shown that for models with chiral three-spin interactions the Dzyaloshinsky-Moriya coupling yields the onset of the weak ferromagnetism, similar to three-dimensional ordered antiferromagnets, but not present in other quantum spin chains with the antisymmetric exchange. Considered models appeared to be important for several quasi-one-dimensional spin systems, studied in recent experiments.
Thermodynamic properties of antiferromagnetic spin chain with various AFM nearest-neighbor and FM next-nearest-neighbor exchange interactions are studied using functional integral method in J 1 – J 2 Heisenberg model. Besides, the excitation spectrum of the system is also given. The results show that the system has two distinct excitations with no energy gap from the ground state for any permissible values of J 1 and J 2 without single-ion anisotropy. Changing the exchange parameters influences on the thermodynamic properties and the excitation spectra of the system.