Extended Luttinger-Tisza analysis of magnetic phases in frustrated honeycomb lattices

This paper presents a numerical investigation of the classical spin-۱/۲ Heisenberg J۱ − J۲ model on thetwo-dimensional honeycomb lattice, primarily utilizing eigenvalue-based methods. We employ both the standard and extended versions of the Luttinger-Tisza method to determine classical ground states and phase transitions as a function of the frustration ratio, J۲/J۱. The standard Luttinger-Tisza method, through Fourier transformation and global spin normalization, reduces the Hamiltonian to an eigenvalue problem in momentum space, thereby enabling the identification of Néel and spiral spin liquid phases. In contrast, the Extended Luttinger-Tisza method, implemented in real space, incorporates permutation operators and coupling matrices defined on multi-spin unit cells, thus facilitating the detection of more complex magnetic orders such as zigzag and stripy phases. Our analysis reveals significant discrepancies between the two methods, particularly in the high-frustration regime (J۲/J۱ >۱/۲),highlighting the necessity of symmetry-adapted real-space computations for accurately characterizing frustrated systems. Beyond J۲/J۱ >۱/۲, the extended method computationally delineates the stripy phase. In contrast, the standard method predicts a Néel phase in this regime, which can be attributed to its global spin normalization constraint. These results illustrate the efficacy of such mathematical and numerical techniques in classifying spin model ground states and provide a robust framework for future analytical and computational studies.

کلیدواژه ها:

Runge-Kutta Method ، Extended Luttinger-Tisza method ، Heisenberg model ، Honeycomb lattice ، Spiral spin liquid