Primary and Secondary Order Parameters in the Fully Frustrated Transverse Field Ising Model on the Square Lattice

Abstract

Using quantum Monte Carlo simulations and field-theory arguments, we study the fully frustrated (Villain) transverse-field Ising model on the square lattice. We consider a "primary" spin order parameter and a "secondary" dimer order parameter, which both lead to the same phase diagram but detect $Z_8$ and $Z_4$ symmetry, respectively. The spin order scales with conventional exponents, both in the finite temperature critical phase and at the $T=0$ quantum critical point. The scaling of the dimer order requires more detailed investigations of the applicable low-energy theories; the height model at $T>0$ and the $O(2)$ model in 2+1 dimensions at $T=0$. Relating the order parameters to operators in these effective models, we predict the secondary critical exponents and confirm them numerically. The relationships between the primary and secondary order parameters have not been previously discussed in this context and provide insight more broadly for Ising models whose low-energy physics involves dimer degrees of freedom.

11 pages, 13 figures

References in corpus (11)

• The critical exponents of the superfluid transition in He4
• Stochastic series expansion method for quantum Ising models with arbitrary interactions
• Interplay of quantum and thermal fluctuations in a frustrated magnet
• Interacting classical dimers on the square lattice
• Monte Carlo study of an improved clock model in three dimensions
• Ordering of geometrically frustrated classical and quantum Ising magnets
• Evidence of columnar order in the fully frustrated transverse field Ising model on the square lattice
• String Picture of a Frustrated Quantum Magnet and Dimer Model
• Quadrupole Orders on the fcc Lattice
• Semiclassical evidence of columnar order in the fully frustrated transverse field Ising model on the square lattice
• Quantum orders in the frustrated Ising model on the bathroom tile lattice

Cited by in corpus (3)

• Quantum Quench Dynamics of Geometrically Frustrated Ising Models
• Zero-temperature Monte Carlo simulations of two-dimensional quantum spin glasses guided by neural network states
• Longitudinal-field fidelity susceptibility analysis of the $J_1$-$J_2$ transverse-field Ising model around $J_2/J_1\approx 0.5$