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The coupled cluster method (CCM) is used to study the zero-temperatureproperties of a frustrated spin-half ($s={1}{2}$) $J_{1}$--$J_{2}$ Heisenbergantiferromagnet (HAF) on a 2D chevron-square lattice. Each site on anunderlying square lattice has 4 nearest-neighbor exchange bonds of strength$J_{1}>0$ and 2 next-nearest-neighbor (diagonal) bonds of strength $J_{2}\equiv x J_{1}>0$, with each square plaquette having only one diagonal bond.The diagonal bonds form a chevron pattern, and the model thus interpolatessmoothly between 2D HAFs on the square ($x=0$) and triangular ($x=1$) lattices,and also extrapolates to disconnected 1D HAF chains ($x \to \infty$). Theclassical ($s \to \infty$) version of the model has N\'{e}el order for $0 < x <x_{{\rm cl}}$ and a form of spiral order for $x_{{\rm cl}} < x < \infty$, where$x_{{\rm cl}} = {1}{2}$. For the $s={1}{2}$ model we use both these classicalstates, as well as other collinear states not realized as classicalground-state (GS) phases, as CCM reference states, on top of which themultispin-flip configurations resulting from quantum fluctuations areincorporated in a systematic truncation scheme, which we carry out to highorders and extrapolate to the physical limit. We calculate the GS energy, GSmagnetic order parameter, and the susceptibilities of the states to variousforms of valence-bond crystalline (VBC) order, including plaquette and twodifferent dimer forms. We find that the $s={1}{2}$ model has two quantumcritical points, at $x_{c_{1}} \approx 0.72(1)$ and $x_{c_{2}} \approx 1.5(1)$,with N\'{e}el order for $0 < x < x_{c_{1}}$, a form of spiral order for$x_{c_{1}} < x < x_{c_{2}}$ that includes the correct three-sublattice$120^{\circ}$ spin ordering for the triangular-lattice HAF at $x=1$, andparallel-dimer VBC order for $x_{c_{2}} < x < \infty$.

A frustrated spin-1/2 Heisenberg antiferromagnet on a chevron-square lattice