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Universality Class of Ising Critical States with Long-Range Losses

2022; American Physical Society; Volume: 129; Issue: 5 Linguagem: Inglês

10.1103/physrevlett.129.050603

1092-0145

Jamir Marino,

Advanced Thermodynamics and Statistical Mechanics

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 $\ensuremath{\propto}{q}^{\ensuremath{\alpha}}$, with $\ensuremath{\alpha}$ a positive tunable exponent directly related to the power-law decay of the spatial profile of losses at long distances, $1/{r}^{(\ensuremath{\alpha}+d)}$. 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 $\ensuremath{\alpha}<1$ we find a nonequilibrium critical point ruled by a dynamical field theory described by a Langevin model with coexisting inertial ($\ensuremath{\sim}{\ensuremath{\partial}}_{t}^{2}$) and frictional ($\ensuremath{\sim}{\ensuremath{\partial}}_{t}$) kinetic coefficients, and driven by a gapless Markovian noise with variance $\ensuremath{\propto}{q}^{\ensuremath{\alpha}}$ 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.