Quantum $J_1$--$J_2$ antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering

TL;DR

This study investigates how interlayer coupling affects magnetic order in a frustrated quantum antiferromagnet, showing that increasing coupling suppresses the disordered phase and promotes magnetic order.

Contribution

It provides a detailed analysis of the impact of interlayer coupling on the ground-state phases of the $J_1$-$J_2$ model using CCM and RGM methods, revealing the disappearance of the disordered phase at moderate coupling.

Findings

Disordered phase shrinks with increasing interlayer coupling.

Quantum paramagnetic phase disappears at $J_ot \,\sim\, 0.2-0.3 J_1$.

Magnetic long-range order persists beyond the disordered phase.

Abstract

Using the coupled-cluster method (CCM) and the rotation-invariant Green's function method (RGM), we study the influence of the interlayer coupling $J_\perp$ on the magnetic ordering in the ground state of the spin-1/2 $J_1$-$J_2$ frustrated Heisenberg antiferromagnet ($J_1$-$J_2$ model) on the stacked square lattice. In agreement with known results for the $J_1$-$J_2$ model on the strictly two-dimensional square lattice ($J_\perp=0$) we find that the phases with magnetic long-range order at small $J_2< J_{c_1}$ and large $J_2> J_{c_2}$ are separated by a magnetically disordered (quantum paramagnetic) ground-state phase. Increasing the interlayer coupling $J_\perp>0$ the parameter region of this phase decreases, and, finally, the quantum paramagnetic phase disappears for quite small $J_\perp \sim 0.2 ... 0.3 J_1$.