Двовимiрна спiн-1/2 J1 − J′1 − J2 модель Гайзенберґа в рамках перетворення Йордана–Вiґнера - Baran, O. R.; Verkholyak, T. M. (Publishing house "Academperiodika", 2019)
The Jordan–Wigner transformation is applied to the spatially anisotropic spin-1/2 Heisenberg model on a square lattice with the nearest-neighbor and next-nearest-neighbor antiferromagnetic interactions. The transformed Hamiltonian describes the interacting spinless fermions that hop between neighbor sites in a gauge field. Using the mean-field-type approximation to both the direct interaction between fermions and the phase factors, which represent the gauge field, the problem is reduced to that concerning a free Fermi gas. Two types of antiferromagnetic ordering (the N´eel and collinear ones) are considered. By calculating the ground-state energies, the phase transitions induced by the interaction frustration were analyzed.