The authors investigate the fate of dissipative phase transitions in quantum many-body systems when the individual constituents are qudits (d-level systems) instead of qubits. As an example system, they employ a permutation-invariant XY model of N infinite-range interacting d-level spins undergoing individual and collective dissipation.
In the mean-field limit, the authors identify a dissipative phase transition, whose critical point is independent of d after a suitable rescaling of parameters. When the decay rates between all adjacent levels are identical and d≥4, the critical point expands to a critical region in which two phases coexist, and this region increases as d grows. Additionally, a larger d leads to a more pronounced change in spin expectation values at the critical point.
Numerical investigations for finite N reveal symmetry breaking signatures in the Liouvillian spectrum at the phase transition. The phase transition is furthermore marked by maximum entanglement negativity and a significant purity change of the steady state, which become more pronounced as d increases.
The authors conclude that considering qudits instead of qubits opens new perspectives on accessing rich phase diagrams in open many-body systems.
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