TY - JOUR

T1 - Tunable Splitting of the Ground-State Degeneracy in Quasi-One-Dimensional Parafermion Systems

AU - Chen, Chun

AU - Burnell, F. J.

PY - 2016/3/10

Y1 - 2016/3/10

N2 - Systems with topologically protected ground-state degeneracies are currently of great interest due to their potential applications in quantum computing. In practice, this degeneracy is never exact, and the magnitude of the ground-state degeneracy splitting imposes constraints on the time scales over which information is topologically protected. In this Letter, we use an instanton approach to evaluate the splitting of topological ground-state degeneracy in quasi-1D systems with parafermion zero modes, in the specific case where parafermions are realized by inducing a superconducting gap in pairs of fractional quantum Hall edges. We show that, like 1D topological superconducting wires, this splitting has an oscillatory dependence on the chemical potential, which arises from an intrinsic Berry phase that produces interference between distinct instanton tunneling events. These Berry phases can be mapped to chiral phases in a (dual) quantum clock model using a Fradkin-Kadanoff transformation. Comparing our low-energy spectrum to that of phenomenological parafermion models allows us to evaluate the real and imaginary parts of the hopping integral between adjacent parafermionic zero modes as functions of the chemical potential.

AB - Systems with topologically protected ground-state degeneracies are currently of great interest due to their potential applications in quantum computing. In practice, this degeneracy is never exact, and the magnitude of the ground-state degeneracy splitting imposes constraints on the time scales over which information is topologically protected. In this Letter, we use an instanton approach to evaluate the splitting of topological ground-state degeneracy in quasi-1D systems with parafermion zero modes, in the specific case where parafermions are realized by inducing a superconducting gap in pairs of fractional quantum Hall edges. We show that, like 1D topological superconducting wires, this splitting has an oscillatory dependence on the chemical potential, which arises from an intrinsic Berry phase that produces interference between distinct instanton tunneling events. These Berry phases can be mapped to chiral phases in a (dual) quantum clock model using a Fradkin-Kadanoff transformation. Comparing our low-energy spectrum to that of phenomenological parafermion models allows us to evaluate the real and imaginary parts of the hopping integral between adjacent parafermionic zero modes as functions of the chemical potential.

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U2 - 10.1103/PhysRevLett.116.106405

DO - 10.1103/PhysRevLett.116.106405

M3 - Article

C2 - 27015499

AN - SCOPUS:84961190352

VL - 116

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 10

M1 - 106405

ER -