Universality class of Ising critical states with long-range losses

TL;DR

This paper demonstrates how spatially resolved dissipation in $d$-dimensional Ising systems can qualitatively alter their critical points, leading to a new universality class characterized by long-range losses and non-unitary critical behavior.

Contribution

It introduces a novel class of non-unitary critical points in Ising models with power-law decaying dissipation, extending the understanding of universality in driven-open quantum systems.

Findings

Identification of a new non-equilibrium critical point for $oldsymbol{oldsymbol{ extit{ extit{ extbf{ extcolor{red}{ ext{}}}}}}}$ with $oldsymbol{oldsymbol{ extit{ extit{ extbf{ extcolor{red}{ ext{}}}}}}}$ $oldsymbol{ extbf{ extcolor{red}{ ext{}}}}$

Derivation of a Langevin model with inertial and frictional terms describing the critical dynamics

Critical exponents differ from those of unitary long-range Ising models.

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.