Finite Temperature Phase Diagram of the Fully Frustrated Transverse Field Ising Model

Using quantum Monte Carlo simulations, we study the fully frustrated transverse field Ising model on the square lattice. This model is defined with ferromagnetic bonds on all rows, but on every other column, with anti-ferromagnetic bonds in their place. This construction makes it impossible satisfy all bonds in an elementary plaquette, providing a rich ground-state degeneracy of the classical model. The addition of a transverse field (Γ) lifts the degeneracy, and the system exhibits “order-by-disorder,” up to a critical value Γ_c, as studied in previous works. We confirm the location and universality class of this quantum phase transition, and further explore the nature of this system at finite T. To do so, we consider two order parameters; based on spins and dimers, with the latter defined on the dual lattice. We find different (but simply related) scaling exponents for these order parameters, and both exhibit a robust, emergent U(1) symmetry that persists deep into the ordered phase up to very large system sizes. While it is numerically challenging to beat this length scale, we show that the 4-fold degenerate, columnar dimer ordering does indeed stabilize by annealing through the critical temperature. We also find that along the finite temperature phase boundary, the value of the critical exponent ν varies continuously, from ν=1 in the limit Γ → Γ_c to ν =∞ in the limit Γ → 0, in analogy to the 2D, four-state classical clock model, which, however, does not exhibit any emergent U(1) symmetry. While the reason behind the emergent symmetry together with varying exponent is unknown, we suggest possible explanations for this behavior.