Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2109.03712 · Physical Review Letters

1/3 Power-Law Universality Class out of Stochastic Driving in Interacting Systems

Zi Cai

Published Feb 2, 2022• 14 citations
arXivHTMLPDF

Abstract

In this Letter, we study the mean-field dynamics of a general class of many-body systems with stochastically fluctuating interactions. Our findings reveal a universal algebraic decay of the order parameter m(t)∼t^{-χ} with an exponent χ=1/3 that is independent of most system details including the strength of the stochastic driving, the energy spectrum of the undriven systems, the initial states, and even the driving protocols. It is shown that such a dynamical universality class can be understood as a consequence of a diffusive process with a time-dependent diffusion coefficient which is determined self-consistently during the evolution. The finite-size effect, as well as the relevance of our results with current experiments in high-finesse cavity QED systems are also discussed.

DOI
10.1103/physrevlett.128.050601

Related papers

A dynamical universality class out of stochastic driving in interacting quantum many-body systems

Zi Cai

In this paper, we study the mean-field dynamics of a general class of quantum many-body systems with stochastically fluctuating interactions. Our findings reveal a universal algebraic decay of the order parameter $m(t)\sim t^{-\chi}$ with an exponent $\chi=\frac 13$ that is independent of most system details including the strength of the stochastic driving, the energy spectrum of the undriven systems, the initial states and even the driving protocols. The finite-size effect, as well as the relevance of our results with current experiments in high-finesse cavity QED systems are also discussed.

•Sep 8, 2021•0 citations

Dynamic scaling relation in quantum many-body systems

Devendra Singh Bhakuni, Yevgeny Bar Lev

In delocalized systems, particle number fluctuations, also known as quantum surface roughness, and the mean-square displacement exhibit a temporal power law growth followed by a saturation to a system size--dependent value. We use simple scaling arguments to show that these quantities satisfy the Family-Vicsek scaling law and derive a dynamic scaling relation between the dynamical exponents, assuming that the saturation times of both quantities scale similarly with the system size. This relation clarifies the mechanism behind quantum surface roughness growth and suggests that diffusive quantum many-body systems belong to the Edwards-Wilkinson universality class. Moreover, it provides a convenient way to assess quantum transport in cold-atoms experiments. We numerically verify our results by studying two noninteracting models and one interacting model having regimes with distinct dynamical exponents.

arXiv:2309.03273•Physical review. B./Physical review. B•Jul 10, 2024•18 citations

Universal Algebraic Growth of Entanglement Entropy in Many-Body Localized Systems with Power-Law Interactions

Xiaolong Deng, Guido Masella, Guido Pupillo +1 more

Power-law interactions play a key role in a large variety of physical systems. In the presence of disorder, these systems may undergo many-body localization for a sufficiently large disorder. Within the many-body localized phase the system presents in time an algebraic growth of entanglement entropy, S_{vN}(t)∝t^{γ}. Whereas the critical disorder for many-body localization depends on the system parameters, we find by extensive numerical calculations that the exponent γ acquires a universal value γ_{c}≃0.33 at the many-body localization transition, for different lattice models, decay powers, filling factors, or initial conditions. Moreover, our results suggest an intriguing relation between γ_{c} and the critical minimal decay power of interactions necessary for many-body localization.

arXiv:1912.08131•Physical Review Letters•Jun 29, 2020•38 citations

Universality Class of Ising Critical States with Long-Range Losses

Jamir Marino

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

arXiv:2108.12422•Physical Review Letters•Jul 29, 2022•23 citations

Nonlinear Fluctuating Hydrodynamics from Interacting Noisy Quantum Matter

Alexios Christopoulos, João Costa, Stefano Scopa +4 more

A universal characterization of non-equilibrium steady states in interacting quantum many-body systems remains one of the central challenges of statistical physics. Here, we address this problem for a paradigmatic model of diffusive interacting quantum matter---the boundary-driven XXZ spin chain with bulk dephasing---and derive, directly from its microscopic Lindblad dynamics, an emergent classical Macroscopic Fluctuation Theory (MFT) governing its large-scale fluctuations. Crucially, the resulting hydrodynamics carries a density-dependent diffusivity and mobility as the fingerprint of interactions. This effective description enables the exact computation of the stationary density profile, long-range correlations, and the full counting statistics of the current, in excellent agreement with tensor-network simulations. Our work demonstrates that noisy quantum many-body systems can realize the universality class of genuinely interacting diffusive matter, beyond the constant-diffusivity class of the symmetric simple exclusion process, and establishes MFT as a powerful universal framework for interacting diffusive quantum systems.

cond-mat.stat-mechCross-listedarXiv:2609.00159•Sep 2, 2026•0 citations

Power-law decay exponents: A dynamical criterion for predicting thermalization

Marco Távora, Eduardo Jonathan Torres-Herrera, Léa Ferreira dos Santos

From the analysis of the relaxation process of isolated lattice many-body quantum systems quenched far from equilibrium, we deduce a criterion for predicting when they are certain to thermalize. It is based on the algebraic behavior $\ensuremath{\propto}{t}^{\ensuremath{-}\ensuremath{\gamma}}$ of the survival probability at long times. We show that the value of the power-law exponent $\ensuremath{\gamma}$ depends on the shape and filling of the weighted energy distribution of the initial state. Two scenarios are explored in detail: $\ensuremath{\gamma}\ensuremath{\ge}2$ and $\ensuremath{\gamma}<1$. Exponents $\ensuremath{\gamma}\ensuremath{\ge}2$ imply that the energy distribution of the initial state is ergodically filled and the eigenstates are uncorrelated, so thermalization is guaranteed to happen. In this case, the power-law behavior is caused by bounds in the energy spectrum. Decays with $\ensuremath{\gamma}<1$ emerge when the energy eigenstates are correlated and signal lack of ergodicity. They are typical of systems undergoing localization due to strong onsite disorder and are found also in clean integrable systems.

arXiv:1610.04240•Physical Review A•Jan 5, 2017•53 citations
In this Letter, we study the mean-field dynamics of a general class of many-body systems with stochastically fluctuating interactions. Our findings reveal a universal algebraic decay of the order parameter m(t)∼t^{-χ} with an exponent χ=1/3 that is independent of most system details including the strength of the stochastic driving, the energy spectrum of the undriven systems, the initial states, and even the driving protocols. It is shown that such a dynamical universality class can be understood as a consequence of a diffusive process with a time-dependent diffusion coefficient which is determined self-consistently during the evolution. The finite-size effect, as well as the relevance of our results with current experiments in high-finesse cavity QED systems are also discussed.
In this paper, we study the mean-field dynamics of a general class of quantum many-body systems with stochastically fluctuating interactions. Our findings reveal a universal algebraic decay of the order parameter m(t)∼t−χm(t)\sim t^{-\chi}m(t)∼t−χ with an exponent χ=13\chi=\frac 13χ=31​ that is independent of most system details including the strength of the stochastic driving, the energy spectrum of the undriven systems, the initial states and even the driving protocols. The finite-size effect, as well as the relevance of our results with current experiments in high-finesse cavity QED systems are also discussed.
In delocalized systems, particle number fluctuations, also known as quantum surface roughness, and the mean-square displacement exhibit a temporal power law growth followed by a saturation to a system size--dependent value. We use simple scaling arguments to show that these quantities satisfy the Family-Vicsek scaling law and derive a dynamic scaling relation between the dynamical exponents, assuming that the saturation times of both quantities scale similarly with the system size. This relation clarifies the mechanism behind quantum surface roughness growth and suggests that diffusive quantum many-body systems belong to the Edwards-Wilkinson universality class. Moreover, it provides a convenient way to assess quantum transport in cold-atoms experiments. We numerically verify our results by studying two noninteracting models and one interacting model having regimes with distinct dynamical exponents.
Power-law interactions play a key role in a large variety of physical systems. In the presence of disorder, these systems may undergo many-body localization for a sufficiently large disorder. Within the many-body localized phase the system presents in time an algebraic growth of entanglement entropy, S_{vN}(t)∝t^{γ}. Whereas the critical disorder for many-body localization depends on the system parameters, we find by extensive numerical calculations that the exponent γ acquires a universal value γ_{c}≃0.33 at the many-body localization transition, for different lattice models, decay powers, filling factors, or initial conditions. Moreover, our results suggest an intriguing relation between γ_{c} and the critical minimal decay power of interactions necessary for many-body localization.
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 ∝q^{α}, with α a positive tunable exponent directly related to the power-law decay of the spatial profile of losses at long distances, 1/r^{(α+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 α<1 we find a nonequilibrium critical point ruled by a dynamical field theory described by a Langevin model with coexisting inertial (∼∂_{t}^{2}) and frictional (∼∂_{t}) kinetic coefficients, and driven by a gapless Markovian noise with variance ∝q^{α} 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.
A universal characterization of non-equilibrium steady states in interacting quantum many-body systems remains one of the central challenges of statistical physics. Here, we address this problem for a paradigmatic model of diffusive interacting quantum matter---the boundary-driven XXZ spin chain with bulk dephasing---and derive, directly from its microscopic Lindblad dynamics, an emergent classical Macroscopic Fluctuation Theory (MFT) governing its large-scale fluctuations. Crucially, the resulting hydrodynamics carries a density-dependent diffusivity and mobility as the fingerprint of interactions. This effective description enables the exact computation of the stationary density profile, long-range correlations, and the full counting statistics of the current, in excellent agreement with tensor-network simulations. Our work demonstrates that noisy quantum many-body systems can realize the universality class of genuinely interacting diffusive matter, beyond the constant-diffusivity class of the symmetric simple exclusion process, and establishes MFT as a powerful universal framework for interacting diffusive quantum systems.
From the analysis of the relaxation process of isolated lattice many-body quantum systems quenched far from equilibrium, we deduce a criterion for predicting when they are certain to thermalize. It is based on the algebraic behavior $\ensuremath{\propto}{t}^{\ensuremath{-}\ensuremath{\gamma}}$ of the survival probability at long times. We show that the value of the power-law exponent $\ensuremath{\gamma}$ depends on the shape and filling of the weighted energy distribution of the initial state. Two scenarios are explored in detail: $\ensuremath{\gamma}\ensuremath{\ge}2$ and $\ensuremath{\gamma}<1$. Exponents $\ensuremath{\gamma}\ensuremath{\ge}2$ imply that the energy distribution of the initial state is ergodically filled and the eigenstates are uncorrelated, so thermalization is guaranteed to happen. In this case, the power-law behavior is caused by bounds in the energy spectrum. Decays with $\ensuremath{\gamma}<1$ emerge when the energy eigenstates are correlated and signal lack of ergodicity. They are typical of systems undergoing localization due to strong onsite disorder and are found also in clean integrable systems.