Emergent Universality Class in Dissipative Quantum Systems with Dipole Moment Conservation

Abstract

Understanding the non-equilibrium dynamics of quantum many-body systems remains one of the grand challenges of modern physics. In particular, increasing attention has been devoted to the emergence of non-equilibrium universality classes that have no equilibrium counterparts. A prominent example is the Kardar-Parisi-Zhang universality class realized in dissipative Bose-Einstein condensates. In this Letter, motivated by recent experimental advances, we investigate the universal dynamics of dissipative quantum systems with dipole moment conservation. We develop an effective field theory description, supported by a concrete quantum spin model, to capture the resulting universal behaviors. Our analysis unveils a novel strongly interacting non-equilibrium fixed point that governs the equal-time phase fluctuations in systems with either strong or weak dipole symmetries. Moreover, charge transport becomes subdiffusive in the presence of strong dipole symmetry, while it remains diffusive in the weakly symmetric case. Our results reveal the intricate interplay between kinetic constraints and dissipation in quantum many-body systems.

Figures (2)

• Figure 1: A schematic of our one-dimensional quantum spin model with dipole moment conservation for $S=1/2$. The system consists of two types of spins, denoted by $s$ and $\Delta$. During the coherent evolution governed by the Hamiltonian, exchanges of $s$ spins are accompanied by flips of the $\Delta$ spins, ensuring the dipole moment conservation. For the dissipative dynamics, we consider several processes that are compatible with this symmetry. We provide examples of dominant dissipation processes that exhibit strong or weak dipole symmetry.
• Figure 2: Numerical simulations of the Langevin equation \ref{['eq:classical']} with $g = 0.5$, $\tilde{D}_2 =0$, $\tilde{D} =1$, and $C = 1$ are performed for different system sizes $L\in\{60,80,100\}$. We plot the results by fixing $z=2$ and using two different exponents: (a) $\chi = 1/2$ and (b) $\chi = 2$. The results clearly demonstrate the emergence of a novel non-equilibrium universality class in the long-time limit.