Quantum and Classical Potts Criticality in Driven-Dissipative Bosonic Lattices

• URL: http://arxiv.org/abs/2607.08425v2
• Date: Fri, 10 Jul 2026 06:54:56 GMT
• Title: Quantum and Classical Potts Criticality in Driven-Dissipative Bosonic Lattices
• Abstract summary: We investigate a Bose-Hubbard lattice subject to three-photon parametric driving.<n>We find that in two-dimensional lattices with single-photon losses, the nonequilibrium steady-state transition belongs to the class of the 2D classical three-state Potts model.<n>In contrast, in one-dimensional lattices with three-photon losses, the transition is governed by the one-dimensional quantum three-state Potts universality class.
• Score: 6.258703171051429
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The emergence of equilibrium universality from intrinsically nonequilibrium dynamics is a fundamental open problem. Bose-Hubbard lattices realized in photonic and circuit-QED platforms provide a versatile setting to engineer nonlinear interactions, dissipation, and multiphoton processes. Here we investigate a Bose-Hubbard lattice subject to three-photon parametric driving, whose nonequilibrium steady state spontaneously breaks a $\mathbb Z_3$ symmetry and realizes the criticality of the three-state Potts model, a three-state generalization of the Ising model. Using a variational phase-space approach with systematically controllable accuracy based on a Variational Multi-Gaussian ansatz, we perform finite-size scaling analyses in one and two spatial dimensions. We find that, in two-dimensional lattices with single-photon losses, the nonequilibrium steady-state transition belongs to the universality class of the 2D classical three-state Potts model. In contrast, in one-dimensional lattices with three-photon losses, the transition is governed by the one-dimensional quantum three-state Potts universality class. These results establish driven-dissipative bosonic lattices as a platform for emergent Potts criticality and identify multiphoton dissipation as a mechanism that promotes nonequilibrium critical behavior from classical to quantum universality classes.

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