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Physical review. B./Physical review. B

Scaling and universality at noise-affected nonequilibrium spin correlation functions

Rouhollah Jafari, Alireza Akbari

Published Jun 11, 2026• 1 citation
Publisher
DOI
10.1103/6d4v-wc93

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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.
We derive a consistent two-loop scaling picture for a Kondo dot in both equilibrium and nonequilibrium situations using the flow equation method. Our analysis incorporates the important decoherence effects from both thermal and nonequilibrium noise in a common setting. In the weak-coupling regime we calculate the spin-spin correlation function, the T-matrix, and the magnetization as functions of applied magnetic field, dc-voltage bias and temperature. In all these quantities we observe characteristic nonequilibrium features for a nonvanishing external voltage bias such as Kondo splitting and strongly enhanced logarithmic corrections.
We solve for the time-dependent finite-size scaling functions of the one-dimensional transverse-field Ising chain during a linear-in-time ramp of the field through the quantum critical point. We then simulate Mott-insulating bosons in a tilted potential, an experimentally studied system in the same equilibrium universality class, and demonstrate that universality holds for the dynamics as well. We find qualitatively athermal features of the scaling functions, such as negative spin correlations, and we show that they should be robustly observable within present cold atom experiments.