Coupled Wire Model of $Z_2\times Z_2$ Orbifold Quantum Hall States

Abstract

We construct a coupled wire model for a sequence of non-Abelian quantum Hall states occurring at filling factors $\nu =2/(2M+q)$ with integers $M$ and even(odd) integers $q$ for fermionic(bosonic) states. They are termed $Z_2\times Z_2$ orbifold states, which have a topological order with a neutral sector described by the $c=1$ orbifold conformal field theory (CFT) at radius $R_{\mathrm{orbifold}}=\sqrt{p/2}$ with even integers $p$. When $p=2$, the state can be viewed as two decoupled layers of Moore-Read (MR) state, whose neutral sector is described by the Ising $\times$ Ising CFT and contains a $Z_2\times Z_2$ fusion subalgebra. We demonstrate that orbifold states with $p>2$, also containing a $Z_2\times Z_2$ fusion algebra, can be obtained by coupling together an array of MR $\times$ MR wires through local interactions. The corresponding charge spectrum of quasiparticles is also examined. The orbifold states constructed here are complementary to the $Z_4$ orbifold states, whose neutral edge theory is described by orbifold CFT with odd integer $p$ and contains a $Z_4$ fusion algebra.

arXiv comment12 pages, 4 figures

References in corpus (13)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• The Fractional Quantum Hall effect in an array of quantum wires
• From Luttinger liquid to non-Abelian quantum Hall states
• Quantum Hall Physics - hierarchies and CFT techniques
• A Web of 2d Dualities: ${\mathbf{Z}}_2$ Gauge Fields and Arf Invariants
• Anyon Condensation and Continuous Topological Phase Transitions in Non-Abelian Fractional Quantum Hall States
• Pairing in Luttinger Liquids and Quantum Hall States
• $U(1)\times U(1)⋊Z_2$ Chern-Simons Theory and Z_4 Parafermion Fractional Quantum Hall States
• Bilayer quantum Hall phase transitions and the orbifold non-Abelian fractional quantum Hall states
• A model of chiral spin liquids with Abelian and non-Abelian topological phases
• Coupled Wire Model of Z4 Orbifold Quantum Hall States

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• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• Dihedral twist liquid models from emergent Majorana fermions
• Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays