Boundary conditions dependence of the phase transition in the quantum Newman-Moore model

Abstract

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 cellular automata methods, we obtain a full characterization of the minimum energy configurations of the TPM for arbitrary tori sizes. For the QTPM, we use these cycle patterns to obtain the symmetries of the model, which we argue determine its quantum phase transition: we find it to be 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 also find that this classification is consistent with exact diagonalization, Matrix Product States and Quantum Monte Carlo simulations.

17 pages, 19 figures: post publication typos fixed

References in corpus (5)

• The density-matrix renormalization group in the age of matrix product states
• Glassy dynamics of kinetically constrained models
• The performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs
• On the path integral representation for quantum spin models and its application to the quantum cavity method and to Monte Carlo simulations
• Transition path sampling algorithm for discrete many-body systems

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