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Jordan–Wigner fermionization for spin-½ systems in two dimensions: A brief review

Oleg Derzhko

We review the papers on the Jordan{Wigner transformation in two dimensions to comment on a possibility of examining the statistical mechanics properties of two{dimensional spin{ 1 2 models.We discuss in some detail the two{dimensional spin{ 1 2 isotropic XY and Heisenberg models.

arXiv:cond-mat/0101188Journal of Physical StudiesJan 1, 200125 citations

THE SPIN-1/2 AND SPIN-1 QUANTUM J1−J′1−J2 HEISENBERG MODELS ON THE SQUARE LATTICE

R. F. Bishop, P. H. Y. Li, R. Darradi +1 more

Recent Progress in Many-Body TheoriesJun 1, 20080 citations

Two-Dimensional Spin-1/2 J1 – J'1 – J2 Heisenberg Model within Jordan–Wigner Transformation

O. R. Baran, Taras Verkholyak

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.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.

Ukrainian Journal of PhysicsJul 1, 20161 citation

2D quantum spin models and Jordan-Wigner fermions

Oleg Derzhko, Johannes Richter, Taras Verkholyak

Czechoslovak Journal of PhysicsJan 1, 20022 citations

A study of the spin-3/2 Blume-Capel model in the transverse field

O. R. Baran, Р. Р. Левицкий

ДОСЛIДЖЕННЯ СПIН-3/2 МОДЕЛI БЛЮМА-КАПЕЛЯ У ПОПЕРЕЧНОМУ ПОЛI О. Р. Баран, Р. Р

Journal of Physical StudiesJan 1, 20121 citation

2-dimensional Heisenberg model v.s. Fermion in Magnetic field

Kazuhiko Sakakibara

物性研究Mar 20, 19940 citations