Non-Abelian Chern-Simons Theory from a Hubbard-like Model

Abstract

Here, we provide a simple Hubbard-like model of spin-$1/2$ fermions that gives rise to the SU(2) symmetric Thirring model that is equivalent, in the low-energy limit, to Yang-Mills-Chern-Simons model. First, we identify the regime that simulates the SU(2) Yang-Mills theory. Then, we suitably extend this model so that it gives rise to the SU(2) level $k$ Chern-Simons theory with $k\ge 2$ that can support non-Abelian anyons. This is achieved by introducing multiple fermionic species and modifying the Thirring interactions, while preserving the SU(2) symmetry. Our proposal provides the means to theoretically and experimentally probe non-Abelian SU(2) level $k$ topological phases.

4.5 pages, 3 figures, published version

References in corpus (11)

• Classification of topological insulators and superconductors in three spatial dimensions
• Non-Abelian Topological Order in S-Wave Superfluids of Ultracold Fermionic Atoms
• Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories
• Quantum Computation Using Vortices and Majorana Zero Modes of a $p_x$ + $i{p}_y$ Superfluid of Fermionic Cold Atoms
• A cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory
• Direct imaging of topological edge states in cold-atom systems
• Cold atom simulation of interacting relativistic quantum field theories
• Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices
• UV fixed-point structure of the three-dimensional Thirring model
• Measuring topology in a laser-coupled honeycomb lattice: From Chern insulators to topological semi-metals
• Non-abelian anyons from degenerate Landau levels of ultracold atoms in artificial gauge potentials

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• Interaction-Dependent Photon-Assisted Tunneling in Optical Lattices: A Quantum Simulator of Strongly-Correlated Electrons and Dynamical Gauge Fields
• Thermalization, Error-Correction, and Memory Lifetime for Ising Anyon Systems
• Classical Simulation of Quantum Error Correction in a Fibonacci Anyon Code
• Interacting second-order topological insulators in one-dimensional fermions with correlated hopping
• (3+1)-dimensional topological quantum field theory from a tight-binding model of interacting spinless fermions
• Continuous error correction for Ising anyons
• Topological Electromagnetic Effects and Higher Second Chern Numbers in Four-Dimensional Gapped Phases
• Non-Relativistic Supergeometry in the Moore-Read Fractional Quantum Hall State
• Effective models of doped quantum ladders of non-Abelian anyons
• Effective field theories for interacting boundaries of 3D topological crystalline insulators through bosonisation
• Emergence of charge density wave and superconducting phase transitions through Lorentz-invariant interactions in the Haldane-Hubbard model
• Emergent Dynamics of Spacetime and Matter from a Topological Phase