Universality Class of Ising Critical States with Long-Range Losses

We show that spatial resolved dissipation can act on d-dimensional spin systems in the Ising universality class by qualitatively modifying the nature of their critical points. We consider power-law decaying spin losses with a Lindbladian spectrum closing at small momenta as proportional to q(alpha), with a a positive tunable exponent directly related to the power-law decay of the spatial profile of losses at long distances, 1/r((a+d)). This yields a class of soft modes asymptotically decoupled from dissipation at small momenta, which are responsible for the emergence of a critical scaling regime ascribable to the nonunitary counterpart of the universality class of long-range interacting Ising models. For alpha < 1 we find a nonequilibrium critical point ruled by a dynamical field theory described by a Langevin model with coexisting inertial (-partial derivative(2)(t)) and frictional (similar to partial derivative(t)) kinetic coefficients, and driven by a gapless Markovian noise with variance proportional to q(alpha) at small momenta. This effective field theory is beyond the Halperin-Hohenberg description of dynamical criticality, and its critical exponents differ from their unitary long-range counterparts. Our Letter lays out perspectives for a revision of universality in driven open systems by employing dark states tailored by programmable dissipation.

Automated summary

We demonstrate that spatial resolved dissipation can alter the critical points of d-dimensional spin systems in the Ising universality class. By considering power-law decaying spin losses, we reveal the existence of soft modes decoupled from dissipation at small momenta, leading to a nonunitary counterpart of long-range interacting Ising models. A nonequilibrium critical point is found for alpha < 1, characterized by a dynamical field theory described by a Langevin model with coexisting inertial and frictional kinetic coefficients, driven by gapless Markovian noise.