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We present a family of electron-based coupled-wire models of bosonic orbifold topological phases, referred to as twist liquids, in two spatial dimensions. All local fermion degrees of freedom are gapped and removed from the topological order by many-body interactions. Bosonic chiral spin liquids and anyonic superconductors are constructed on an array of interacting wires, each supports emergent massless Majorana fermions that are non-local (fractional) and constitute the S O ( N ) Kac-Moody Wess-Zumino-Witten algebra at level 1. We focus on the dihedral D k symmetry of S O ( 2 n ) 1 , and its promotion to a gauge symmetry by manipulating the locality of fermion pairs. Gauging the symmetry (sub)group generates the C / G twist liquids, where G = Z 2 for C = U ( 1 ) l , S U ( n ) 1 , and G = Z 2 , Z k , D k for C = S O ( 2 n ) 1 . We construct exactly solvable models for all of these topological states. We prove the presence of a bulk excitation energy gap and demonstrate the appearance of edge orbifold conformal field theories corresponding to the twist liquid topological orders. We analyze the statistical properties of the anyon excitations, including the non-Abelian metaplectic anyons and a new class of quasiparticles referred to as Ising-fluxons. We show an eight-fold periodic gauging pattern in S O ( 2 n ) 1 / G by identifying the non-chiral components of the twist liquids with discrete gauge theories. 

We investigate the homogeneous chiral edge theory of the filling ν = 4 / 3 fractional quantum Hall state, which is parameterized by a Luttinger liquid velocity matrix and an electron tunneling amplitude (ignoring irrelevant terms). We identify two solvable cases: one case where the theory gives two free chiral boson modes, and the other case where the theory yields one free charge 2 e 3 chiral fermion and two free chiral Bogoliubov (Majorana) fermions. For generic parameters, the energy spectrum from our exact diagonalization shows Poisson level spacing statistics (LSS) in each conserved charge and momentum sector, indicating the existence of hidden conserved quantities and the possibility that the generic edge theory of the ν = 4 / 3 fractional quantum Hall state is integrable. We further show that a global symmetry preserving irrelevant nonlinear kinetic term will lead to the transition of LSS from Poisson to Wigner-Dyson at high energies. This further supports the possibility that the model without irrelevant terms is integrable.