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Holographic Theory of Mixed-Dimensional Statistics and Conservation-Encoding Hopping-Operator Algebras
Hanyu Xue, Xiao-Gang Wen
We develop a general framework for the statistics of mixed-dimensional excitations subject to intertwined conservation laws, extending the familiar Fermi statistics with conserved…
A Lattice Chiral Boson Theory in d
Michael DeMarco, Ethan Lake, Xiao-Gang Wen
Chiral field theories describe large classes of matter, from the edges of Quantum Hall systems to the electroweak sector of the Standard Model, but defining them on the lattice has…
Exact emergent higher-form symmetries in bosonic lattice models
Salvatore D. Pace, Xiao-Gang Wen
Although condensed matter systems usually do not have higher-form symmetries, we show that, unlike 0-form symmetry, higher-form symmetries can emerge as exact symmetries at low ene…
Emergent generalized symmetry and maximal symmetry-topological-order
Arkya Chatterjee, Wenjie Ji, Xiao-Gang Wen
A characteristic property of a gapless liquid state is its emergent symmetry and dual symmetry, associated with the conservation laws of symmetry charges and symmetry defects respe…
Holographic theory for continuous phase transitions -- the emergence and symmetry protection of gaplessness
Arkya Chatterjee, Xiao-Gang Wen
Two global symmetries are holo-equivalent if their algebras of local symmetric operators are isomorphic. Holo-equivalent classes of global symmetries are classified by gappable-bou…
The boundaries of 2+1D fermionic topological orders
Chang-Han Chen, Xiao-Gang Wen
D bosonic topological orders can be characterized by the matrices that encode the statistics of topological excitations. In particular, the matrices can be used to…
Position-Dependent Excitations and UV/IR Mixing in the Rank-2 Toric Code and its Low-Energy Effective Field Theory
Salvatore D. Pace, Xiao-Gang Wen
We investigate how symmetry and topological order are coupled in the d rank-2 toric code for general , which is an exactly solvable point in the Higgs ph…
Symmetry as a shadow of topological order and a derivation of topological holographic principle
Arkya Chatterjee, Xiao-Gang Wen
Symmetry is usually defined via transformations described by a (higher) group. But a symmetry really corresponds to an algebra of local symmetric operators, which directly constrai…
Topological Mott Insulators and Discontinuous -Terms
Michael A. DeMarco, Ethan Lake, Xiao-Gang Wen
We introduce a lattice field theory that describes the transition between a superfluid (SF) and a bosonic topological Mott Insulator (tMI) -- a symmetry protected topologica…
3+1d Boundaries with Gravitational Anomaly of 4+1d Invertible Topological Order for Branch-Independent Bosonic Systems
Zheyan Wan, Juven Wang, Xiao-Gang Wen
We study bosonic systems on a spacetime lattice defined by path integrals of commuting fields. We introduce branch-independent bosonic (BIB) systems, whose path integral is indepen…
One dimensional gapped quantum phases and enriched fusion categories
Liang Kong, Xiao-Gang Wen, Hao Zheng
In this work, we use Ising chain and Kitaev chain to check the validity of an earlier proposal in arXiv:2011.02859 that enriched fusion (higher) categories provide a unified catego…
A unified view on symmetry, anomalous symmetry and non-invertible gravitational anomaly
Wenjie Ji, Xiao-Gang Wen
In this paper, using 1+1D models as examples, we study symmetries and anomalous symmetries via multi-component partition functions obtained through symmetry twists, and their trans…
A Commuting Projector Model with a Non-zero Quantized Hall conductance
Michael DeMarco, Xiao-Gang Wen
By ungauging a recently discovered lattice rotor model for Chern-Simons theory, we create an exactly soluble path integral on spacetime lattice for Symmetry Protected Topo…
Low energy effective field theories of fermion liquids and mixed anomaly
Xiao-Gang Wen
In this paper we study gapless fermionic and bosonic systems in -dimensional continuum space with particle-number conservation and translation symmetry. We…
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 $…
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…
Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Wenjie Ji, Xiao-Gang Wen
For a zero-temperature Landau symmetry breaking transition in -dimensional space that completely breaks a finite symmetry , the critical point at the transition has the symme…
Metallic states beyond Tomonaga-Luttinger liquids in one dimension
Wenjie Ji, Xiao-Gang Wen
In this paper, we propose some new strongly correlated gapless states (or critical states) of spin-1/2 electrons in 1+1-dimensions, such as doped anti-ferromagnetic spin-1/2 Ising…
Gapped domain walls between 2+1D topologically ordered states
Tian Lan, Xueda Wen, Liang Kong +1
The 2+1D topological order can be characterized by the mapping-class-group representations for Riemann surfaces of genus-1, genus-2, etc. In this paper, we use those representation…
Topological Transition on the Conformal Manifold
Wenjie Ji, Shu-Heng Shao, Xiao-Gang Wen
Despite great successes in the study of gapped phases, a comprehensive understanding of the gapless phases and their transitions is still under developments. In this paper, we stud…
Distinguish modular categories and 2+1D topological orders beyond modular data: Mapping class group of higher genus manifold
Xueda Wen, Xiao-Gang Wen
It was believed that modular data are enough to distinguish different modular categories (and topological orders in 2+1-dimensions). Then counterexamples to this conjecture were fo…
Lattice models that realize -1-symmetry protected topological states for even
Lokman Tsui, Xiao-Gang Wen
Higher symmetries can emerge at low energies in a topologically ordered state with no symmetry, when some topological excitations have very high energy scales while other topologic…