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arXiv · 2405.01223

Dissipative phase transition: from qubits to qudits

Lukas Pausch·François Damanet·Thierry Bastin·John Martin
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Abstract

We 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, we employ a permutation-invariant $XY$ model of $N$ infinite-range interacting $d$-level spins undergoing individual and collective dissipation. In the mean-field limit, we 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 $d\geq 4$, the critical point expands, in terms of the ratio between dissipation and interaction strengths, to a critical region in which two phases coexist and which increases as $d$ grows. In addition, 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. Considering qudits instead of qubits thus opens new perspectives on accessing rich phase diagrams in open many-body systems.

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Lukas Pausch, François Damanet, Thierry Bastin, John Martin. 2024-05-02. Dissipative phase transition: from qubits to qudits. https://doi.org/10.1103/physreva.110.062208

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