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Anyons in an exactly solved model and beyond
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abstract
A spin 1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved exactly by a reduction to free fermions in a static $\mathbb{Z}_{2}$ gauge field. A phase diagram in the parameter space is obtained. One of the phases has an energy gap and carries excitations that are Abelian anyons. The other phase is gapless, but acquires a gap in the presence of magnetic field. In the latter case excitations are non-Abelian anyons whose braiding rules coincide with those of conformal blocks for the Ising model. We also consider a general theory of free fermions with a gapped spectrum, which is characterized by a spectral Chern number $\nu$. The Abelian and non-Abelian phases of the original model correspond to $\nu=0$ and $\nu=\pm 1$, respectively. The anyonic properties of excitation depend on $\nu\bmod 16$, whereas $\nu$ itself governs edge thermal transport. The paper also provides mathematical background on anyons as well as an elementary theory of Chern number for quasidiagonal matrices.
Forward citations
Cited by 31 Pith papers
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Magnetic fields in monoclinic $\alpha$-RuCl$_3$ reveal rhombohedral inclusions underlying apparent oscillations
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Exactly Solvable Topological Phase Transition in a Quantum Dimer Model
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SymTFT actions, Condensable algebras and Categorical anomaly resolutions
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Quasiparticle tunnelling in two coupled chiral SYK model
Two weakly coupled chiral SYK models in 1+1 dimensions stay gapless and show massless collective tunneling modes, with no temperature-dependent free-energy correction at leading order.
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Evidence of chiral fermion edge modes through geometric engineering of thermal Hall in $\alpha$-RuCl$_3$
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The $S=\frac{1}{2}$ XY and XYZ models on the two or higher dimensional hypercubic lattice do not possess nontrivial local conserved quantities
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Operational Tube-Sector Theory of Quantum State Distinguishability Under Generalized Symmetries
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Constructs Z_N extended fusion rings and modular partition functions for nonanomalous subgroups, extending to multicomponent systems and orbifoldings in CFTs.
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Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
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Absence of nontrivial local conserved quantities in the quantum compass model on the square lattice
The quantum compass model on the square lattice possesses no nontrivial local conserved quantities besides the Hamiltonian.
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New classes of boundary and coupled conformal field theories are constructed from Z_N gauging, with a proposed dictionary to topological order, nonchiral anyons, and domain walls.
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