Persisting topological order via geometric frustration

Abstract

We introduce a toric code model on the dice lattice which is exactly solvable and displays topological order at zero temperature. In the presence of a magnetic field, the flux dynamics is mapped to the highly frustrated transverse field Ising model on the kagome lattice. This correspondence suggests an intriguing disorder by disorder phenomenon in a topologically ordered system implying that the topological order is extremely robust due to the geometric frustration. Furthermore, a connection between fully frustrated transverse field Ising models and topologically ordered systems is demonstrated which opens an exciting physical playground due to the interplay of topological quantum order and geometric frustration.

References in corpus (12)

• Short-ranged RVB physics, quantum dimer models and Ising gauge theories
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Low-energy effective theory of the toric code model in a parallel field
• Robustness of a perturbed topological phase
• Topological multicritical point in the Toric Code and 3D gauge Higgs Models
• Self-duality and bound states of the toric code model in a transverse field
• Adiabatic Preparation of Topological Order
• Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: doubled Chern-Simons theory
• Phase diagram of the toric code model in a parallel magnetic field
• Interplay of Topological Order and Spin Glassiness in the Toric Code under Random Magnetic Fields
• Disorder by disorder and flat bands in the kagome transverse field Ising model
• Evidence of columnar order in the fully frustrated transverse field Ising model on the square lattice

Cited by in corpus (20)

• Order-by-disorder and spin-orbital liquids in a distorted Heisenberg-Kitaev model
• Intrinsic quantum Ising model on a triangular lattice magnet TmMgGaO${}_4$ and beyond
• Quantum robustness of fracton phases
• Frustrated topological symmetry breaking: geometrical frustration and anyon condensation
• Quantum critical phase transition between two topologically-ordered phases in the Ising toric code bilayer
• High-order series expansion of non-Hermitian quantum spin models
• Quantum phase transitions out of a Z2 x Z2 topological phase
• Ising order parameter and topological phase transitions: Toric code in a uniform magnetic field
• Topological line in frustrated Toric code models
• Full characterization of a spin liquid phase: from topological entropy to robustness and braid statistics
• Quantum phase transition as an interplay of Kitaev and Ising interactions
• Quantum disorder and local modes of the fully-frustrated transverse field Ising model on a diamond chain
• Quantum phase transitions in the $K$-layer Ising toric code
• Quantum robustness of the toric code in a parallel field on the honeycomb and triangular lattice
• Fracton and topological order in the XY checkerboard toric code
• Partially topological phase in a quantum loop gas model with tension and pressure
• Quantum phase transitions to topological Haldane phases in spin-one chains studied by linked-cluster expansions
• Frustrated mixed-spin ladders: Evidence for a bond order wave phase between rung-singlet and Haldane phases
• ParaToric 1.0: Continuous-time quantum Monte Carlo for the toric code in a parallel field
• Duality in spin systems via the $SU(4)$ algebra