Universality class of Ising critical states with long-range losses
- URL: http://arxiv.org/abs/2108.12422v2
- Date: Fri, 29 Jul 2022 16:36:18 GMT
- Title: Universality class of Ising critical states with long-range losses
- Authors: Jamir Marino
- Abstract summary: We show that spatial resolved dissipation can act on $d$-dimensional spin systems in the Ising universality class.
We consider power-law decaying spin losses with a Lindbladian spectrum closing at small momenta as $propto qalpha$.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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 $\propto q^\alpha$, with
$\alpha$ a positive tunable exponent directly related to the power-law decay of
the spatial profile of losses at long distances, $1/r^{(\alpha+d)}$. 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 non-unitary counterpart of the universality class of
long-range interacting Ising models. For $\alpha<1$ we find a non-equilibrium
critical point ruled by a dynamical field theory described by a Langevin model
with coexisting inertial ($\sim {\partial^2_t}$) and frictional ($\sim
{\partial_t}$) kinetic coefficients, and driven by a gapless Markovian noise
with variance $\propto q^\alpha$ 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 work
lays out perspectives for a revision of universality in driven-open systems by
employing dark states taylored by programmable dissipation.
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