Dimer Expansion Study of the Bilayer Square Lattice Frustrated Quantum Heisenberg Antiferromagnet

Abstract

The ground state of the square lattice bilayer quantum antiferromagnet with nearest ($J_1$) and next-nearest ($J_2$) neighbour intralayer interaction is studied by means of the dimer expansion method up to the 6-th order in the interlayer exchange coupling $J_3$. The phase boundary between the spin-gap phase and the magnetically ordered phase is determined from the poles of the biased Padé approximants for the susceptibility and the inverse energy gap assuming the universality class of the 3-dimensional classical Heisenberg model. For weak frustration, the critical interlayer coupling decreases linearly with $\alpha (=J_2/J_1)$. The spin-gap phase persists down to $J_3=0$ (single layer limit) for $0.45 \simleq α\simleq 0.65$. The crossover of the short range order within the disordered phase is also discussed.

4 pages, 6 figures, One reference added

References in corpus (2)

• Various series expansions for the bilayer S=1/2 Heisenberg antiferromagnet
• Phase Transitions in Bilayer Heisenberg Model with General Couplings

Cited by in corpus (4)

• Quantum impurity dynamics in two-dimensional antiferromagnets and superconductors
• Interlayer Coupling Effect on a Bilayer Kitaev Model
• Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on a square-lattice bilayer: High-order study of the quantum critical behavior of the $J_1$--$J_2$--$J_1^{\perp }$ model
• Ground-state properties for bilayer Kitaev model: dimer expansion study