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Spin Dynamics in the 2-site cluster Heisenberg antiferromagnet.

Omamoke O. E. Enaroseha, Olusola Oyebola

Published Jul 18, 2023• 3 citations
Publisher

Abstract

The spin -½ Heisenberg antiferromagnet Hamiltonian with exchange integral and applied external magnetic field is studied with the help of direct exact diagonalization technique. Two site cluster lattices with open boundary conditions are considered and the criteria for the occurrence of a transition from antiferromagnetic (AFM) phase to a ferromagnetic (FM) phase are discussed.However, the results obtained shows that the temperature dependence of the uniform magnetization depends on the strength of the applied magnetic field h. If the applied magnetic field is smaller than the critical field strength, the zero temperature magnetization vanishes, otherwise it is activated.

DOI
10.31219/osf.io/xur9y

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The magnetic and thermodynamic properties of 13-atom clusters with decahedral and layered geometries have been studied with spin-1/2 using the quantum Heisenberg model. The numerical exact diagonalization technique is applied to solve the quantumspin Hamiltonian for both ferro (FM) and anti-ferromagnetic (AFM) interactions of the clusters. The ground state energies for the FM case are found to be all degenerate while for the AFM case, they are non-degenerate. In the presence of external magnetic field, we found discontinuities in the field-dependent magnetization accompanied by plateaus for the AFM interaction. The thermodynamic entities such as entropy and specific heat as a function of external magnetic field are smeared out with increasing temperature. They also show a strong dependence on the cluster geometry.
We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (J1FJ_1^FJ1F​) and antiferromagnetic (J1AJ_1^AJ1A​) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction (J2FJ_2^FJ2F​). In this model frustration is induced by the non-zero J2FJ_2^FJ2F​ and the effect of dimerization is realized by changing the strength of J1AJ_1^AJ1A​ for a fixed value of J1FJ_1^FJ1F​. The model with site spin sss behaves like a Haldane spin chain with site spin 2sss in the limit of vanishing J2FJ_2^FJ2F​ and large J1F/J1AJ_1^F/J_1^AJ1F​/J1A​. We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of J1A−J2FJ_1^A-J_2^FJ1A​−J2F​ is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.
We study the quantum critical behavior in the antiferromagnetic Heisenberg chain and two-leg Heisenberg ladder resulting from the application of an external magnetic field. In each of these systems a finite-temperature crossover line between two different ferromagnetic phases ends with a quantum critical point at zero temperature. Using the bond-mean-field theory, we calculate the field dependence of the magnetization and the mean-field spin bond parameters in both systems. For the Heisenberg chain, we recover the existing exact results and show in addition that the saturation of the zero-temperature magnetization at the field hc=2J{h}_{c}=2Jhc​=2J is accompanied by a quantum phase transition, where the bond parameter vanishes. Here JJJ is the exchange coupling constant along the chain. For the two-leg ladder, we also recover the known results, like the two magnetization plateaus, and show that at the upper critical field, which corresponds to the appearance of the saturation magnetization plateau, the chain and rung spin bond parameters vanish. The identification of the order parameters that govern the field-induced quantum criticality in the systems we study here constitutes an original contribution. Because no long-range order, which breaks symmetry, characterizes the bond order, the latter could be a proposal for the so-called hidden order. We calculate analytically the bond parameters in both systems as functions of the field in the low- and high-field limits at zero temperature. At nonzero temperatures, the calculation of the magnetization and bond parameters is carried out by solving the mean-field equations numerically.
Motivated by the numerical simulation of systems which display quantum phase transitions, we present a novel application of the meron-cluster algorithm to simulate the quantum antiferromagnetic Heisenberg model coupled to an external uniform magnetic field both in one and in two dimensions.In the infinite volume limit and at zero temperature we found numerical evidence that supports a quantum phase transition very close to the critical values B c = 2 and B c = 4 for the system in one and two dimensions, respectively.For the one dimensional system, we have compared the numerical data obtained with analytical predictions for the magnetization density as a function of the external field obtained by scaling-behaviour analysis and Bethe Ansatz techniques.Since there is no analytical solution for the two dimensional case, we have compared our results with the magnetization density obtained by scaling relations for small lattice sizes and with the approximated thermodynamical limit at zero temperature guessed by scaling relations.Moreover, we have compared the numerical data with other numerical simulations performed by using different algorithms in one and two dimensions, like the directed loop method.The numerical data obtained are in perfect agreement with all these previous results, which confirms that the meron-algorithm is reliable for quantum Monte Carlo simulations and applicable both in one and two dimensions.Finally, we have computed the integrated autocorrelation time to measure the efficiency of the meron algorithm in one dimension.