Kavli Affiliate: Matthew P. A. Fisher
| First 5 Authors: DinhDuy Vu, Ali Lavasani, Jong Yeon Lee, Matthew P. A. Fisher,
| Summary:
The Floquet code utilizes a periodic sequence of two-qubit measurements to
realize the topological order. After each measurement round, the instantaneous
stabilizer group can be mapped to a honeycomb toric code, explaining the
topological feature. The code also possesses a time-crystal order – the $e-m$
transmutation after every cycle, breaking the Floquet symmetry of the
measurement schedule. This behavior is distinct from the stationary topological
order realized in either random circuits or time-independent Hamiltonian.
Therefore, the resultant phase belongs to the overlap between the classes of
Floquet enriched topological orders and measurement-induced phases. In this
work, we construct a continuous path interpolating between the Floquet and
toric codes, focusing on the transition between the time-crystal and stationary
topological phases. We show that this transition is characterized by a
divergent length scale. We also add single-qubit perturbations to the model and
obtain a richer two-dimensional parametric phase diagram of the Floquet code,
showing the stability of the Floquet enriched topological order.
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