Dissipative phase transition: from qubits to qudits

TL;DR

This paper explores how dissipative phase transitions in quantum many-body systems evolve when replacing qubits with qudits, revealing expanded critical regions and richer phase behavior as the local system dimension increases.

Contribution

It demonstrates that increasing the local dimension to qudits enlarges the critical region and enhances phase transition signatures in dissipative quantum systems.

Findings

Critical point is independent of $d$ after rescaling.

Critical region expands for $d extgreater= 4$ with increasing $d$.

Enhanced entanglement and purity changes at the transition for larger $d$.

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.