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

  • O. R. Baran Institute for Condensed Matter Physics, Nat. Acad. of Sci. of Ukraine
  • T. M. Verkholyak Institute for Condensed Matter Physics, Nat. Acad. of Sci. of Ukraine
Keywords: two-dimensional quantum spin models, frustrated models, fermionization

Abstract

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.

Published
2019-01-05
How to Cite
Baran, O., & Verkholyak, T. (2019). Two-Dimensional Spin-1/2 J1 − J′1 − J2 Heisenberg Model within Jordan–Wigner Transformation. Ukrainian Journal of Physics, 61(7), 597. https://doi.org/10.15407/ujpe61.07.0597
Section
Solid matter