Activated dynamics in the quantum random field Ising model
Abstract
We study the critical dynamics of the quantum random-field Ising model using the nonperturbative functional renormalization group (NP-FRG). The static critical behavior is found to be controlled by the zero-temperature fixed point of the classical random-field Ising model, where both thermal and quantum fluctuations are dangerously irrelevant. Considering a family of quantum dynamical universality classes defined by a bare dynamical kernel F Λ (ω) ∼ |ω| σ , we show how this fluctuationless fixed point nevertheless controls the quantum dynamics by computing the full Matsubara-frequency dependence of the running dynamical kernel F k (ω). This is essential at zero temperature: a naive treatment of the dynamical kernel flow leads to a divergence at a finite length scale, resulting in apparent localization. In contrast, keeping the full frequency dependence of the dynamical kernel and choosing a regulator adapted to its running scale yields a controlled flow.
The resulting dynamics is of activated form, with a relaxation time given by ln τ ∼ ξ Ψ . The exponent Ψ is determined by the static RFIM fixed-point exponents and by σ. At finite temperature, the flow crosses over to the classical thermally activated scaling of the random-field Ising model.
These results provide a quantitative field-theoretic realization of the heuristic activation scenario proposed earlier for the quantum random-field model and establish a framework for analyzing the dynamics of other disordered quantum systems that may exhibit similar tentative localization-like singularities.
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BibTeX
@misc{balog2026activated,
title = {{Activated dynamics in the quantum random field Ising model}},
author = {Ivan Balog and Lovro Šaravanja and Andrei Fedorenko},
howpublished = {HAL},
year = {2026},
month = jun,
eprint = {2606.31663},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05850775v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Activated dynamics in the quantum random field Ising model
AU - Ivan Balog
AU - Lovro Šaravanja
AU - Andrei Fedorenko
PY - 2026
DA - 2026/06/30
PB - HAL
UR - https://hal.science/hal-05850775v1
AB - We study the critical dynamics of the quantum random-field Ising model using the nonperturbative functional renormalization group (NP-FRG). The static critical behavior is found to be controlled by the zero-temperature fixed point of the classical random-field Ising model, where both thermal and quantum fluctuations are dangerously irrelevant. Considering a family of quantum dynamical universality classes defined by a bare dynamical kernel F Λ (ω) ∼ |ω| σ , we show how this fluctuationless fixed point nevertheless controls the quantum dynamics by computing the full Matsubara-frequency dependence of the running dynamical kernel F k (ω). This is essential at zero temperature: a naive treatment of the dynamical kernel flow leads to a divergence at a finite length scale, resulting in apparent localization. In contrast, keeping the full frequency dependence of the dynamical kernel and choosing a regulator adapted to its running scale yields a controlled flow. The resulting dynamics is of activated form, with a relaxation time given by ln τ ∼ ξ Ψ . The exponent Ψ is determined by the static RFIM fixed-point exponents and by σ. At finite temperature, the flow crosses over to the classical thermally activated scaling of the random-field Ising model. These results provide a quantitative field-theoretic realization of the heuristic activation scenario proposed earlier for the quantum random-field model and establish a framework for analyzing the dynamics of other disordered quantum systems that may exhibit similar tentative localization-like singularities.
ER -