Evidence of columnar order in the fully frustrated transverse field Ising model on the square lattice

Abstract

Using extensive classical and quantum Monte Carlo simulations, we investigate the ground-state phase diagram of the fully frustrated transverse field Ising model on the square lattice. We show that pure columnar order develops in the low-field phase above a surprisingly large length scale, below which an effective U(1) symmetry is present. The same conclusion applies to the Quantum Dimer Model with purely kinetic energy, to which the model reduces in the zero-field limit, as well as to the stacked classical version of the model. By contrast, the 2D classical version of the model is shown to develop plaquette order. Semiclassical arguments show that the transition from plaquette to columnar order is a consequence of quantum fluctuations.

5 pages (including Supplemental Material), 5 figures

References in corpus (5)

• The critical exponents of the superfluid transition in He4
• Interplay of quantum and thermal fluctuations in a frustrated magnet
• Quantum Dimer Model on the triangular lattice: Semiclassical and variational approaches to vison dispersion and condensation
• Efficient Monte Carlo algorithm in quasi-one-dimensional Ising spin systems
• Superfluid Insulator Transitions of Hard-Core Bosons on the Checkerboard Lattice

Cited by in corpus (13)

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• Phase Diagram of the Easy-Axis Triangular-Lattice $J_1-J_2$ Model
• Unconventional U(1) to ${\mathbf{Z}}_{\mathbf{q}}$ cross-over in quantum and classical $\mathbf{q}$-state clock models
• Semiclassical evidence of columnar order in the fully frustrated transverse field Ising model on the square lattice
• Edge modes in a frustrated quantum Ising chain
• Spinless fermions in a ${\mathbb{Z}}_2$ gauge theory on the triangular ladder
• Primary and Secondary Order Parameters in the Fully Frustrated Transverse Field Ising Model on the Square Lattice
• Quantum orders in the frustrated Ising model on the bathroom tile lattice
• Quantum selection of order and dynamic properties of Kitaev-Heisenberg ferromagnet on a triangular lattice
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