Phase Transitions and Edge States in Fluxonium Qubit Systems

A chain of fluxonium qubits provides the means for simulating quantum many-body phenomena in spin-1/2 magnets. The available controls allow us to map a qubit chain on an Ising chain in a transverse magnetic field with variable parameters. The role of the transverse field is played by the tunnel-induced splitting between the lowest energy states at the half-flux sweet spot [1]. The interaction comes from the inductive qubit coupling between fluxoniums' superinductors and can exceed the level splitting [2]. The magnetic flux detuning from the sweet spot plays the role of the longitudinal field for an Ising spin. In this talk, we discuss the phase diagram of the fluxonium chain. We demonstrate the quantum phase transition with the varying level splitting and the emergence of the edge states. We compare these states to the Majorana states in a fermion chain. We study how the edge state localization length depends on the disorder in the random longitudinal and transverse fields.

[1] Lin et al, Phys. Rev. Lett. 120, 150503 (2018).
[2] Kou et al. Phys. Rev. X 7, 031037 (2017).