Interacting Anyonic Fermions in a Two-Body Color Code Model

Abstract

We introduce a two-body quantum Hamiltonian model of spin-1/2 on a 2D spatial lattice with exact topological degeneracy in all coupling regimes. There exists a gapped phase in which the low-energy sector reproduces an effective color code model. High energy excitations fall into three families of anyonic fermions that turn out to be strongly interacting. The model exhibits a Z_2xZ_2 gauge group symmetry and string-net integrals of motion, which are related to the existence of topological charges that are invisible to moving high-energy fermions.

RevTeX 4, 2 figures, longer version

References in corpus (11)

• A toolbox for lattice spin models with polar molecules
• Topological Quantum Distillation
• An exact chiral spin liquid with non-Abelian anyons
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
• Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net Condensates
• Fractionalization, topological order, and quasiparticle statistics
• Mosaic spin models with topological order
• Perturbative approach to an exactly solved problem: the Kitaev honeycomb model
• Creation and Manipulation of Anyons in the Kitaev Model
• Spectrum of the non-abelian phase in Kitaev's honeycomb lattice model

Cited by in corpus (29)

• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Prediction of Toric Code Topological Order from Rydberg Blockade
• Topological insulators and fractional quantum Hall effect on the ruby lattice
• Topological Subsystem Codes
• Universal topological phase of 2D stabilizer codes
• Permutation-invariant quantum codes
• Pauli stabilizer models of twisted quantum doubles
• A Noisy Approach to Intrinsically Mixed-State Topological Order
• Towards a classification of mixed-state topological orders in two dimensions
• Pauli topological subsystem codes from Abelian anyon theories
• Robustness of a topological phase: Topological color code in parallel magnetic field
• Infinite Projected Entangled-Pair State algorithm for ruby and triangle-honeycomb lattices
• Engineering 3D Floquet codes by rewinding
• Topological Color Codes and Two-Body Quantum Lattice Hamiltonians
• Generalized Toric Codes Coupled to Thermal Baths
• Quantum phase transitions out of a Z2 x Z2 topological phase
• A complete characterization of the spectrum of the Kitaev model on spin ladders
• Topological spin liquids in the ruby lattice with anisotropic Kitaev interactions
• Topological ${\mathbb{Z}}_2$ RVB quantum spin liquid on the ruby lattice
• 3-Fermion topological quantum computation
• $Z_3$ generalization of the Kitaev's spin-1/2 model
• Exact Chiral Spin Liquids and Mean-Field Perturbations of Gamma Matrix Models on the Ruby Lattice
• 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
• Finite temperature topological order in 2D topological color codes
• Designing ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ topological orders in networks of Majorana bound states
• Thermal stability of two-dimensional Topological Color Code
• Wire Codes
• Implementation of Single-qubit and CNOT Gates by Anyonic Excitations of Two-body Topological Color Code