Gapped paramagnetic state in a frustrated spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the cross-striped square lattice

Abstract

We implement the coupled cluster method to very high orders of approximation to study the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$ Heisenberg model on a cross-striped square lattice. Every nearest-neighbour pair of sites on the square lattice has an isotropic antiferromagnetic exchange bond of strength $J_{1}>0$, while the basic square plaquettes in alternate columns have either both or neither next-nearest-neighbour (diagonal) pairs of sites connected by an equivalent frustrating bond of strength $J_{2} \equiv αJ_{1} > 0$. By studying the magnetic order parameter (i.e., the average local on-site magnetization) in the range $0 \leq α\leq 1$ of the frustration parameter we find that the quasiclassical antiferromagnetic Néel and (so-called) double Néel states form the stable ground-state phases in the respective regions $α< α_{1a}^{c} = 0.46(1)$ and $α> α_{1b}^{c} = 0.615(5)$. The double Néel state has Néel ($\cdots\uparrow\downarrow\uparrow\downarrow\cdots$) ordering along the (column) direction parallel to the stripes of squares with both or no $J_{2}$ bonds, and spins alternating in a pairwise ($\cdots\uparrow\uparrow\downarrow\downarrow\uparrow\uparrow\downarrow\downarrow\cdots$) fashion along the perpendicular (row) direction, so that the parallel pairs occur on squares with both $J_{2}$ bonds present. Further explicit calculations of both the triplet spin gap and the zero-field uniform transverse magnetic susceptibility provide compelling evidence that the ground-state phase over all or most of the intermediate regime $α_{1a}^{c} < α< α_{1b}^{c}$ is a gapped state with no discernible long-range magnetic order.