Quantum Newman-Moore model in a longitudinal field

We study the quantum Newman-Moore model, or quantum triangular plaquette model (qTPM), in the presence of a longitudinal field (qTPMz). We present evidence that indicates that the ground state phase diagram of the qTPMz includes various frustrated phases breaking translational symmetries, dependent on the specific sequence of system sizes used to take the large-size limit. This phase diagram includes the known first-order phase transition of the qTPM, but also additional first-order transitions due to the frustrated phases. Using the average longitudinal magnetization as an order parameter, we analyze the magnetization plateaus that characterize the ground state phases, describe their degeneracies, and obtain the qTPMz phase diagram using classical transfer matrix and quantum matrix product state techniques. We identify a region of the parameter space, which can be effectively described by a Rydberg blockade model on the triangular lattice. At the same time, it can be reformulated as an effective lattice gauge theory but also a model of quantum trimers. In this same region, we provide a variational ground state wave function similar to a resonating valence bond solid state, which accurately describes the ground state wave function of the system. Lastly, we fail to find indications of a phase with <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi mathvariant="double-struck">Z</a:mi><a:mn>2</a:mn></a:msub></a:math> topological order connecting the quantum paramagnetic and classical frustrated phases.