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:2602.10805

Scaling and Universality at Noise-Affected Non-Equilibrium Spin Correlation Functions

R. Jafari, Alireza Akbari

cond-mat.stat-mechcond-mat.str-elquant-phSubmitted Feb 11, 2026• Announced Feb 12, 2026• 0 citations
arXivHTMLPDF

Abstract

We investigate scaling and universality in nonequilibrium spin correlation functions in the presence of uncorrelated noise. In the absence of noise, spin correlation functions exhibit a crossover from monotonic decay at fast sweep velocities to oscillatory behavior at slow sweeps. We show that, under a stochastically driven field, the critical sweep velocity at which the spin correlation functions undergo an abrupt change decreases with increasing noise strength and scales linearly with the square of the noise intensity. Remarkably, when the noise intensity and sweep velocity are comparable, the excitation probability becomes locked to pk = 1/2 over a finite momentum window, signaling the emergence of noise-induced maximally mixed modes. This gives rise to a highly oscillatory region in the dynamical phase diagram, whose threshold sweep velocity increases with noise and likewise exhibits quadratic scaling with the noise strength. Finally, we identify a universal scaling function under which all boundary sweep-velocity curves collapse onto a single universal curve.

Related papers

Scaling and universality at noisy quench dynamical quantum phase transitions

Saeid Ansari, Rouhollah Jafari, Alireza Akbari +1 more

Dynamical quantum phase transitions (DQPTs) have been studied in the extended X Y model under both noiseless and noisy linear driven staggered field cases. In the time-independent staggered field case, the model exhibits a single critical point where the transition occurs from the spin-liquid phase to the antiferromagnetic phase. In the noiseless ramp case, unlike the transverse field X Y model where DQPT always occurs for a quench crossing the single critical point, there is a critical sweep velocity above which the kinks corresponding to a DQPT are completely removed. Furthermore, in this case there are only two critical modes whose excitation probability is one-half. In the presence of a Gaussian white noise, we find that this critical sweep velocity decreases by increasing the noise strength, and scales linearly with the square of the noise intensity. A surprising result occurs when the noise intensity and sweep velocity are about the same order of magnitude: The number of critical modes is significantly increased, signaling a region with multiple critical modes. Furthermore, our findings indicate that the scaling of the dynamical free energy near the DQPT time is the same for both noiseless and noisy ramp quenches.

arXiv:2506.14355•Physical review. B./Physical review. B•Jul 15, 2025•7 citations

Dynamics of decoherence in a noisy driven environment

Rouhollah Jafari, Ali Asadian, Mehdi Abdi +1 more

We analyze the decoherence dynamics of a central spin coupled to a spin chain with a time-dependent noisy magnetic field, focusing on how noise influences the system's decoherence. Our results show that decoherence due to the nonequilibrium critical dynamics of the environment is amplified in the presence of uncorrelated and correlated Gaussian noise. We demonstrate that decoherence factor consistently signals the critical points, and exhibits exponential scaling with the system size, the square of noise intensity, and the noise correlation time at the critical points. We find that strong coupling between the qubit and the environment leads to partial revivals of decoherence, which diminish with increasing noise intensity or decreasing noise correlation time. In contrast, weak coupling leads to monotonic enhanced decoherence. The numerical results illustrate that, the revivals decay and scale exponentially with noise intensity. Moreover, the revivals increase and indicate linear or power law scaling with noise correlation time depending on how the correlated noise is fast or slow. Additionally, we explore the non-Markovianity of the dynamics, finding that it decays in the presence of noise but increases as the noise correlation time grows.

arXiv:2409.01375•Scientific Reports•May 13, 2025•5 citations

Universal driven critical dynamics across a quantum phase transition in ferromagnetic spinor atomic Bose-Einstein condensates

Ming Xue, Shuai Yin, Li You

We study the equilibrium and dynamical properties of a ferromagnetic spinor atomic Bose-Einstein condensate. In the vicinity of the critical point for a continuous quantum phase transition, universal behaviors are observed both in the equilibrium state and in the dynamics when the quadratic Zeeman shift is swept linearly. Three distinct dynamical regions are identified for different sweeping time scales ($\ensuremath{\tau}$) when compared to the time scale ${\ensuremath{\tau}}_{\mathrm{KZ}}\ensuremath{\sim}{N}^{(1+\ensuremath{\nu}z)/\ensuremath{\nu}d}$ decided by external driving in a system with finite size $N$ ($\ensuremath{\nu},z$ are critical exponents and $d$ the dimensionality). They are manifested by the excitation probability $\mathcal{P}$ and the excess heat density $\mathcal{Q}$. The adiabatic region of $\mathcal{P}\ensuremath{\sim}\mathcal{Q}\ensuremath{\sim}{\ensuremath{\tau}}^{\ensuremath{-}2}$ follows from the adiabatic perturbation theory when $\ensuremath{\tau}>{\ensuremath{\tau}}_{\mathrm{KZ}}$, while the nonadiabatic universal region of $\mathcal{P}\ensuremath{\sim}\mathcal{Q}\ensuremath{\sim}{\ensuremath{\tau}}^{\ensuremath{-}1}$ in the thermodynamic limit is described by the Kibble-Zurek mechanism when ${\ensuremath{\tau}}_{\mathrm{KZ}}>\ensuremath{\tau}>$ the time scale given by initial gap. The Kibble-Zurek scaling hypothesis is augmented with finite-size scaling in the latter region and several experimentally falsifiable features for the finite system we consider are predicted. The region of the fastest sweeping is found to be nonuniversal and far from equilibrium, with $\mathcal{P}$ and $\mathcal{Q}$ essentially being constants independent of $\ensuremath{\tau}$.

arXiv:1805.02174•Physical Review A•Jul 17, 2018•30 citations

Dynamical Phase diagram of the Quantum Ising model with Cluster Interaction Under Noisy and Noiseless Driven field

Sasan Kheiri, Rouhollah Jafari, S. Mahdavifar +2 more

In most lattice models, gap closing typically occurs at high-symmetry points in the Brillouin zone. In the transverse field Ising model with cluster interaction, besides the gap closing at high-symmetry points, the gap closing at the quantum phase transition between paramagnetic and cluster phases of the model can be moved by tuning the strength of the cluster interaction. We take advantage of this property to examine the nonequilibrium dynamics of the model in the framework of dynamical quantum phase transitions (DQPTs) after a noiseless and noisy ramp of the transverse magnetic field. The numerical results show that DQPTs always happen if the starting or ending point of the quench field is restricted between two critical points. In other ways, there is always critical sweep velocity above which DQPTs disappear. Our finding reveals that noise modifies drastically the dynamical phase diagram of the model. We find that the critical sweep velocity decreases by enhancing the noise intensity and scales linearly with the square of noise intensity for weak and strong noise. Moreover, the region with multi-critical modes induced in the dynamical phase diagram by noise. The sweep velocity under which the system enters the multi-critical modes (MCMs) region increases by enhancing the noise and scales linearly with the square of noise intensity

arXiv:2506.14372•Jun 17, 2025•0 citations

Dynamical phase diagram of the quantum Ising model with cluster interaction under noiseless and noisy driven field

Sasan Kheiri, Rouhollah Jafari, S. Mahdavifar +2 more

In most lattice models, gap closing typically occurs at high-symmetry points in the Brillouin zone. In the transverse field Ising model with cluster interaction, the gap closes at high-symmetry points, as well as at the phase transition between paramagnetic and cluster phases, where the gap-closing mode can be moved by tuning the strength of the cluster interaction. We take advantage of this property to examine the nonequilibrium dynamics of the model in the framework of dynamical quantum phase transitions (DQPTs) after a noiseless and noisy ramp of the transverse magnetic field. The numerical results show that DQPTs always happen if the starting or ending point of the quench field is restricted between two critical points. In other ways, there is always critical sweep velocity above which DQPTs disappear. Our finding reveals that noise modifies drastically the dynamical phase diagram of the model. We find that the critical sweep velocity decreases by enhancing the noise intensity and scales linearly with the square of noise intensity for weak and strong noise. Moreover, the region with multi-critical modes (MCMs) induced in the dynamical phase diagram by noise. The sweep velocity under which the system enters the MCMs region increases by enhancing the noise and scales linearly with the square of noise intensity.

Scientific Reports•Dec 22, 2025•3 citations

Topological Defects from Quantum Reset Dynamics

R. Jafari, Henrik Johannesson, Sebastian Eggert

We analyze mechanisms for universal out-of-equilibrium dynamics near criticality by exploring the effect of randomized quantum resetting (QR) under a finite-time quench across a quantum phase transition. Using the transverse-field Ising chain as a generic model and exploiting its exact solution, QR is found to cause a crossover of the scaling of the topological defect density with the time scale $τ$ of the quench, from Kibble-Zurek to anti-Kibble-Zurek scaling as $τ$ increases. This reflects a competition between non-adiabatic quench-driven excitations and QR, giving rise to local minima of the defect densities at optimal annealing times. These times and the corresponding local minima are shown to scale as universal power laws with the rate of QR. Additional results for the scaling of the mean excess energy suggest that a system driven across a quantum critical point exhibits the same scaling behavior under a linear quench with QR as with uncorrelated noise.

cond-mat.stat-mechCross-listedarXiv:2602.00230•Physical review. B./Physical review. B•Feb 3, 2026•2 citations
We investigate scaling and universality in nonequilibrium spin correlation functions in the presence of uncorrelated noise. In the absence of noise, spin correlation functions exhibit a crossover from monotonic decay at fast sweep velocities to oscillatory behavior at slow sweeps. We show that, under a stochastically driven field, the critical sweep velocity at which the spin correlation functions undergo an abrupt change decreases with increasing noise strength and scales linearly with the square of the noise intensity. Remarkably, when the noise intensity and sweep velocity are comparable, the excitation probability becomes locked to pk = 1/2 over a finite momentum window, signaling the emergence of noise-induced maximally mixed modes. This gives rise to a highly oscillatory region in the dynamical phase diagram, whose threshold sweep velocity increases with noise and likewise exhibits quadratic scaling with the noise strength. Finally, we identify a universal scaling function under which all boundary sweep-velocity curves collapse onto a single universal curve.
Dynamical quantum phase transitions (DQPTs) have been studied in the extended X Y model under both noiseless and noisy linear driven staggered field cases. In the time-independent staggered field case, the model exhibits a single critical point where the transition occurs from the spin-liquid phase to the antiferromagnetic phase. In the noiseless ramp case, unlike the transverse field X Y model where DQPT always occurs for a quench crossing the single critical point, there is a critical sweep velocity above which the kinks corresponding to a DQPT are completely removed. Furthermore, in this case there are only two critical modes whose excitation probability is one-half. In the presence of a Gaussian white noise, we find that this critical sweep velocity decreases by increasing the noise strength, and scales linearly with the square of the noise intensity. A surprising result occurs when the noise intensity and sweep velocity are about the same order of magnitude: The number of critical modes is significantly increased, signaling a region with multiple critical modes. Furthermore, our findings indicate that the scaling of the dynamical free energy near the DQPT time is the same for both noiseless and noisy ramp quenches.
We analyze the decoherence dynamics of a central spin coupled to a spin chain with a time-dependent noisy magnetic field, focusing on how noise influences the system's decoherence. Our results show that decoherence due to the nonequilibrium critical dynamics of the environment is amplified in the presence of uncorrelated and correlated Gaussian noise. We demonstrate that decoherence factor consistently signals the critical points, and exhibits exponential scaling with the system size, the square of noise intensity, and the noise correlation time at the critical points. We find that strong coupling between the qubit and the environment leads to partial revivals of decoherence, which diminish with increasing noise intensity or decreasing noise correlation time. In contrast, weak coupling leads to monotonic enhanced decoherence. The numerical results illustrate that, the revivals decay and scale exponentially with noise intensity. Moreover, the revivals increase and indicate linear or power law scaling with noise correlation time depending on how the correlated noise is fast or slow. Additionally, we explore the non-Markovianity of the dynamics, finding that it decays in the presence of noise but increases as the noise correlation time grows.
We study the equilibrium and dynamical properties of a ferromagnetic spinor atomic Bose-Einstein condensate. In the vicinity of the critical point for a continuous quantum phase transition, universal behaviors are observed both in the equilibrium state and in the dynamics when the quadratic Zeeman shift is swept linearly. Three distinct dynamical regions are identified for different sweeping time scales ($\ensuremath{\tau}$) when compared to the time scale ${\ensuremath{\tau}}_{\mathrm{KZ}}\ensuremath{\sim}{N}^{(1+\ensuremath{\nu}z)/\ensuremath{\nu}d}$ decided by external driving in a system with finite size NNN ($\ensuremath{\nu},z$ are critical exponents and ddd the dimensionality). They are manifested by the excitation probability P\mathcal{P}P and the excess heat density Q\mathcal{Q}Q. The adiabatic region of $\mathcal{P}\ensuremath{\sim}\mathcal{Q}\ensuremath{\sim}{\ensuremath{\tau}}^{\ensuremath{-}2}$ follows from the adiabatic perturbation theory when $\ensuremath{\tau}>{\ensuremath{\tau}}_{\mathrm{KZ}}$, while the nonadiabatic universal region of $\mathcal{P}\ensuremath{\sim}\mathcal{Q}\ensuremath{\sim}{\ensuremath{\tau}}^{\ensuremath{-}1}$ in the thermodynamic limit is described by the Kibble-Zurek mechanism when ${\ensuremath{\tau}}_{\mathrm{KZ}}>\ensuremath{\tau}>$ the time scale given by initial gap. The Kibble-Zurek scaling hypothesis is augmented with finite-size scaling in the latter region and several experimentally falsifiable features for the finite system we consider are predicted. The region of the fastest sweeping is found to be nonuniversal and far from equilibrium, with P\mathcal{P}P and Q\mathcal{Q}Q essentially being constants independent of $\ensuremath{\tau}$.
In most lattice models, gap closing typically occurs at high-symmetry points in the Brillouin zone. In the transverse field Ising model with cluster interaction, besides the gap closing at high-symmetry points, the gap closing at the quantum phase transition between paramagnetic and cluster phases of the model can be moved by tuning the strength of the cluster interaction. We take advantage of this property to examine the nonequilibrium dynamics of the model in the framework of dynamical quantum phase transitions (DQPTs) after a noiseless and noisy ramp of the transverse magnetic field. The numerical results show that DQPTs always happen if the starting or ending point of the quench field is restricted between two critical points. In other ways, there is always critical sweep velocity above which DQPTs disappear. Our finding reveals that noise modifies drastically the dynamical phase diagram of the model. We find that the critical sweep velocity decreases by enhancing the noise intensity and scales linearly with the square of noise intensity for weak and strong noise. Moreover, the region with multi-critical modes induced in the dynamical phase diagram by noise. The sweep velocity under which the system enters the multi-critical modes (MCMs) region increases by enhancing the noise and scales linearly with the square of noise intensity
In most lattice models, gap closing typically occurs at high-symmetry points in the Brillouin zone. In the transverse field Ising model with cluster interaction, the gap closes at high-symmetry points, as well as at the phase transition between paramagnetic and cluster phases, where the gap-closing mode can be moved by tuning the strength of the cluster interaction. We take advantage of this property to examine the nonequilibrium dynamics of the model in the framework of dynamical quantum phase transitions (DQPTs) after a noiseless and noisy ramp of the transverse magnetic field. The numerical results show that DQPTs always happen if the starting or ending point of the quench field is restricted between two critical points. In other ways, there is always critical sweep velocity above which DQPTs disappear. Our finding reveals that noise modifies drastically the dynamical phase diagram of the model. We find that the critical sweep velocity decreases by enhancing the noise intensity and scales linearly with the square of noise intensity for weak and strong noise. Moreover, the region with multi-critical modes (MCMs) induced in the dynamical phase diagram by noise. The sweep velocity under which the system enters the MCMs region increases by enhancing the noise and scales linearly with the square of noise intensity.
We analyze mechanisms for universal out-of-equilibrium dynamics near criticality by exploring the effect of randomized quantum resetting (QR) under a finite-time quench across a quantum phase transition. Using the transverse-field Ising chain as a generic model and exploiting its exact solution, QR is found to cause a crossover of the scaling of the topological defect density with the time scale τττ of the quench, from Kibble-Zurek to anti-Kibble-Zurek scaling as τττ increases. This reflects a competition between non-adiabatic quench-driven excitations and QR, giving rise to local minima of the defect densities at optimal annealing times. These times and the corresponding local minima are shown to scale as universal power laws with the rate of QR. Additional results for the scaling of the mean excess energy suggest that a system driven across a quantum critical point exhibits the same scaling behavior under a linear quench with QR as with uncorrelated noise.