Symmetry protected (SPT) and symmetry enriched topological (SET) phases of matter are of great interest in condensed matter physics due to new materials such as topological insulators. The Levin–Wen (LW) model for spin/boson systems is an important rigorously solvable model for studying 2D topological phases. The input data for the LW model is a unitary fusion category, but the same model also works for unitary multi-fusion categories. In this paper, we provide the details for this extension of the LW model, and show that the extended LW model is a natural playground for the theoretical study of SPT and SET phases of matter.Symmetry protected (SPT) and symmetry enriched topological (SET) phases of matter are of great interest in condensed matter physics due to new materials such as topological insulators. The Levin–Wen (LW) model for spin/boson systems is an important rigorously solvable model for studying 2D topological phases. The input data for the LW model is a unitary fusion category, but the same model also works for unitary multi-fusion categories. In this paper, we provide the details for this extension of the LW model, and show that the extended LW model is a natural playground for the theoretical study of SPT and SET phases of matter.

arXiv:1412.6589Journal of Physics A Mathematical and TheoreticalMar 2, 201526 citations

The entanglement structure of topological quantum phases

Michael Mariën

Jan 1, 20160 citations

Condensation of achiral simple currents in topological lattice models: Hamiltonian study of topological symmetry breaking

F. J. Burnell, Steven H. Simon, Johannes K. Slingerland

We describe a family of phase transitions connecting phases of differing nontrivial topological order by explicitly constructing Hamiltonians of the Levin-Wen [Levin and Wen, Phys. Rev. B 71, 045110 (2005)] type which can be tuned between two solvable points, each of which realizes a different topologically ordered phase. We show that the low-energy degrees of freedom near the phase transition can be mapped onto those of a Potts model, and we discuss the stability of the resulting phase diagram to small perturbations about the model. We further explain how the excitations in the condensed phase are formed from those in the original topological theory, some of which are split into multiple components by condensation, and we discuss the implications of our results for understanding the nature of general achiral topological phases in 2 $+$ 1 dimensions in terms of doubled Chern-Simons theories.We describe a family of phase transitions connecting phases of differing nontrivial topological order by explicitly constructing Hamiltonians of the Levin-Wen [Levin and Wen, Phys. Rev. B 71, 045110 (2005)] type which can be tuned between two solvable points, each of which realizes a different topologically ordered phase. We show that the low-energy degrees of freedom near the phase transition can be mapped onto those of a Potts model, and we discuss the stability of the resulting phase diagram to small perturbations about the model. We further explain how the excitations in the condensed phase are formed from those in the original topological theory, some of which are split into multiple components by condensation, and we discuss the implications of our results for understanding the nature of general achiral topological phases in 2 $+$ 1 dimensions in terms of doubled Chern-Simons theories.

arXiv:1104.1701Physical Review BSep 16, 2011103 citations

Ground-state degeneracy in the Levin-Wen model for topological phases

Yuting Hu, Spencer D. Stirling, Yong-Shi Wu

We study the properties of topological phases by calculating the ground-state degeneracy (GSD) of the two-dimensional Levin-Wen (LW) model. Here it is explicitly shown that the GSD depends only on the spatial topology of the system. Then we show that the ground state on a sphere is always nondegenerate. Moreover, we study an example associated with a quantum group, and show that the GSD on a torus agrees with that of the doubled Chern-Simons theory, which is consistent with the conjectured equivalence between the LW model associated with a quantum group and the doubled Chern-Simons theory.We study the properties of topological phases by calculating the ground-state degeneracy (GSD) of the two-dimensional Levin-Wen (LW) model. Here it is explicitly shown that the GSD depends only on the spatial topology of the system. Then we show that the ground state on a sphere is always nondegenerate. Moreover, we study an example associated with a quantum group, and show that the GSD on a torus agrees with that of the doubled Chern-Simons theory, which is consistent with the conjectured equivalence between the LW model associated with a quantum group and the doubled Chern-Simons theory.

arXiv:1105.5771Physical Review BFeb 7, 201283 citations

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1 dimensions in terms of doubled Chern-Simons theories.