Disorder from disorder in a strongly frustrated transverse-field Ising chain

We study a one-dimensional chain of comer-sharing triangles with antiferromagnetic Ising interactions along its bonds. Classically, this system is highly frustrated with an extensive entropy at T = 0 and exponentially decaying spin correlations. We show that the introduction of a quantum dynamics via a transverse magnetic field removes the entropy and opens a gap, but leaves the ground state disordered at all values of the transverse field, thereby providing a particularly simple realization of the "disorder by disorder" scenario first proposed by Fazekas and Anderson in their search for resonating valence bond states. Our conclusion relies on exact diagonalization calculations as well as on the analysis of a 14th-order perturbation expansion about the large transverse field limit. This test of the perturbation expansion method suggests that it could be applied to studies of frustrated transverse-field magnets in higher dimensions.