A new sign-problem-free lattice Hamiltonian realizes the S3 quantum double with electric-magnetic duality as translation, yielding a tetracritical Ising boundary and three predicted topological transitions.
Anyon Condensation and Continuous Topological Phase Transitions in Non-Abelian Fractional Quantum Hall States
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abstract
We find a series of possible continuous quantum phase transitions between fractional quantum Hall (FQH) states at the same filling fraction in two-component quantum Hall systems. These can be driven by tuning the interlayer tunneling and/or interlayer repulsion. One side of the transition is the Halperin (p,p,p-3) Abelian two-component state while the other side is the non-Abelian Z4 parafermion (Read-Rezayi) state. We predict that the transition is a continuous transition in the 3D Ising class. The critical point is described by a Z2 gauged Ginzburg-Landau theory. These results have implications for experiments on two-component systems at \nu = 2/3 and single-component systems at \nu = 8/3.
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Self-dual $S_3$ gauge theory in 2+1d: lattice model and topological phase transitions
A new sign-problem-free lattice Hamiltonian realizes the S3 quantum double with electric-magnetic duality as translation, yielding a tetracritical Ising boundary and three predicted topological transitions.