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Quantization of Chern-Simons topological invariants for H-type and L-type quantum systems
Oscar Randal-Williams, Lokman Tsui, Xiao-Gang Wen
In 2+1-dimensions (2+1D), a gapped quantum phase with no symmetry (i.e. a topological order) can have a thermal Hall conductance , where the dimensi…
Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry
Liang Kong, Tian Lan, Xiao-Gang Wen +2
We introduce the notion of algebraic higher symmetry, which generalizes higher symmetry and is beyond higher group. We show that an algebraic higher symmetry in a bosonic system in…
A relation between chiral central charge and ground state degeneracy in 2+1-dimensional topological orders
Liang Kong, Xiao-Gang Wen
A bosonic topological order on -dimensional closed space may have degenerate ground states. The space with different shapes (different metrics) form a moduli space $…
Classification of topological phases with finite internal symmetries in all dimensions
Liang Kong, Tian Lan, Xiao-Gang Wen +2
We develop a mathematical theory of symmetry protected trivial (SPT) orders and anomaly-free symmetry enriched topological (SET) orders in all dimensions via two different approach…
A systematic construction of gapped non-liquid states
Xiao-Gang Wen
Gapped non-liquid state (also known as fracton state) is a very special gapped quantum state of matter that is characterized by a microscopic cellular structure. Such microscopic c…