Boundary conditions dependence of the phase transition in the quantum Newman-Moore model
Konstantinos Sfairopoulos, Luke Causer, Jamie F. Mair, Juan P. Garrahan · Physical review. B./Physical review. B · 2023
We study the triangular plaquette model (TPM), also known as the Newman-Moore model, in the presence of a transverse magnetic field on a lattice with periodic boundaries in both spatial dimensions. We consider specifically the approach to the ground state phase transition of this quantum TPM (QTPM), or quantum Newman-Moore model, as a function of the system size and type of boundary conditions. Using methods based on cellular automata, we obtain a characterization of the minimum energy configurations of the TPM for numerically accessible tori sizes. For the QTPM, we use these cycle patterns to obtain the symmetries of the model which, we argue, indicate the nature of its quantum phase transition: we always identify it as a first-order phase transition, with the addition of spontaneous symmetry breaking for system sizes which have degenerate classical ground states. For sizes accessible to numerics, we corroborate our findings with exact diagonalization, matrix product states, and quantum Monte Carlo simulations.