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 $J_2\equiv \alpha J_1>0$. By studying the magnetic order parameter (i.e., the average local on-site magnetization) in the range $0\le \alpha \le 1$ 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 $\alpha <{\alpha }_{1a}^c=0.46(1)$ and $\alpha >{\alpha }_{1b}^c=0.615(5)$. 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 ${\alpha }_{1a}^c<\alpha <{\alpha }_{1b}^c$ is a gapped state with no discernible long-range magnetic order.

References in corpus (12)

• Quantum magnetism and criticality
• Plaquette valence bond solid in the frustrated Heisenberg quantum antiferromagnet on the square lattice
• Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment
• The J1-J2 model: First order phase transition versus deconfinement of spinons
• Quantum Spin Liquid in Spin 1/2 J1-J2 Heisenberg Model on Square Lattice: Many-Variable Variational Monte Carlo Study Combined with Quantum-Number Projections
• Quantum $J_1$--$J_2$ antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering
• Effect of anisotropy on the ground-state magnetic ordering of the spin-half quantum $J_1^{XXZ}$--$J_2^{XXZ}$ model on the square lattice
• The spin-1/2 square-lattice J_1-J_2 model: The spin-gap issue
• The frustrated Heisenberg antiferromagnet on the checkerboard lattice: the $J_1$--$J_2$ model
• Spin susceptibility of quantum magnets from high to low temperatures
• Simulating a two-dimensional frustrated spin system with fermionic resonating-valence-bond states
• Resonating valence bond trial wave functions with both static and dynamically determined Marshall sign structure

Cited by in corpus (2)

• A high-order study of the quantum critical behavior of a frustrated spin-$\frac{1}{2}$ antiferromagnet on a stacked honeycomb bilayer
• Collinear antiferromagnetic phases of a frustrated spin-$\frac{1}{2}$ $J_1$--$J_2$--$J_1^{\perp }$ Heisenberg model on an $AA$-stacked bilayer honeycomb lattice