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arxiv: 2605.04294 · v1 · submitted 2026-05-05 · ❄️ cond-mat.mtrl-sci

Spin Dynamics from Atomistic Quantum Simulations

Enrico Drigo , Marquis M. McMillan , Benjamin Pingault , Yinan Dong , F. Joseph Heremans , David D. Awschalom , Giulia Galli This is my paper

Pith reviewed 2026-05-08 17:07 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords spin dynamicsKubo theorymachine learningab initioNV centerspin relaxationdecoherencediamond
0
0 comments X p. Extension

The pith

Kubo linear-response theory gives T1 and T2 directly from correlation functions of spin-lattice couplings evaluated on machine-learned trajectories.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows how to express the spin relaxation time T1 and the decoherence time T2 as integrals over time-correlation functions of the spin-lattice interaction. These correlation functions are computed from classical molecular-dynamics trajectories whose spin-lattice coupling values are supplied by machine-learning models trained on ab-initio electronic-structure data. The resulting parameter-free predictions are then compared with new experimental T1 measurements on the nitrogen-vacancy center in diamond and agree closely. A reader would care because the approach supplies a concrete route to forecast the high-temperature performance of spin defects without resorting to fully quantum dynamical simulations.

Core claim

Using Kubo linear-response theory, expressions for T1 and T2 are derived in terms of the correlation functions of the spin-lattice couplings. These functions are obtained from molecular-dynamics runs in which the required time series are generated by state-of-the-art machine-learning models trained on ab-initio data. For the NV center in diamond the computed T1 values match the measured values.

What carries the argument

Kubo linear-response expressions that convert spin-lattice coupling correlation functions into T1 and T2, with the time series produced by machine-learning models trained on ab-initio calculations.

If this is right

  • T1 and T2 become computable without empirical fitting parameters once the correlation functions are available.
  • Classical molecular dynamics supplemented by machine-learned couplings extends the reachable temperature range beyond direct quantum methods.
  • The same framework applies in principle to any optically active spin defect for which ab-initio training data can be generated.
  • Agreement with NV-center data supports replacing phenomenological relaxation models with atomistic correlation-function calculations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The correlation-function route could be reused for other dynamical quantities such as phonon sideband shapes or strain-induced shifts.
  • Varying the molecular-dynamics temperature and pressure would yield explicit temperature and strain maps of T1 and T2 without new experiments.
  • Transferability tests on other host lattices would reveal how far the machine-learning models generalize beyond the training set.

Load-bearing premise

The machine-learning models trained on ab-initio data must generate spin-lattice interaction time series that remain accurate at the temperatures of interest.

What would settle it

A clear mismatch between the T1 computed from the correlation functions and the experimentally measured T1 for the NV center would show that the method does not yet capture the relevant dynamics.

Figures

Figures reproduced from arXiv: 2605.04294 by Benjamin Pingault, David D. Awschalom, Enrico Drigo, F. Joseph Heremans, Giulia Galli, Marquis M. McMillan, Yinan Dong.

Figure 2
Figure 2. Figure 2: Convergence analysis of T1 as a function of the num￾ber of atoms in the simulation cell and segment size used in the block analysis. All calculations are performed using 16 ns NVE molecular dynamics simulations with machine learned potentials at 500 K. 16 ns–long trajectories are collected in the NVE ensem￾ble. From the ZFS time-series obtained with the MACE MLIP and the ZFS NN model, we compute spin–latti… view at source ↗
Figure 4
Figure 4. Figure 4: Spin-lattice relaxation, view at source ↗
Figure 5
Figure 5. Figure 5: Eq. (A9) as a function of temperature for view at source ↗
Figure 6
Figure 6. Figure 6: Eq. (A11) as a function of temperature for view at source ↗
read the original abstract

Optically active solid-state spin defects are promising candidates for quantum applications, however a unified theoretical framework to predict their spin dynamics at high temperatures is not yet available. Here, using Kubo linear--response theory, we derive expressions of spin-lattice and decoherence times \(T_1\) and \(T_2\) in terms of correlation functions of spin--lattice couplings. We then evaluate \(T_1\) and \(T_2\) from molecular dynamics and spin--lattice interaction time--series generated by state--of--the--art machine learning models trained on {\it ab--initio} data. Finally we measure \(T_1\) times for the NV center in diamond and compare experimental and theoretical results, showing excellent agreement.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper derives expressions for spin-lattice relaxation time T1 and decoherence time T2 using Kubo linear-response theory in terms of correlation functions of spin-lattice couplings. These are evaluated numerically from molecular-dynamics trajectories of spin-lattice interactions generated by machine-learning models trained on ab-initio data. The framework is applied to the NV center in diamond, where predicted T1 values are compared directly to new experimental measurements and reported to show excellent agreement.

Significance. If the ML-generated time series faithfully reproduce the relevant spectral densities, the approach supplies a unified, largely parameter-free route from ab-initio data to high-temperature spin dynamics for solid-state defects. The direct experimental comparison for NV T1 is a concrete strength that would make the method useful for quantum-device design.

major comments (1)
  1. [computational pipeline / NV-center results] The computational pipeline section (following the Kubo derivation): the substitution of ML-interpolated spin-lattice coupling time series for direct ab-initio sampling is load-bearing for the NV-center T1 comparison, yet no separate validation is provided that these trajectories reproduce the phonon-resolved spectral density of the couplings at the experimental temperatures and relevant frequencies. Any systematic bias in the learned forces or matrix elements would propagate directly into the integrated correlation functions that determine the predicted T1.
minor comments (2)
  1. [Kubo derivation] Notation for the correlation functions C(t) and the precise definition of the spectral density J(ω) should be stated explicitly in the derivation section to avoid ambiguity when the expressions are evaluated numerically.
  2. [results / abstract] The abstract states 'excellent agreement' with experiment; the main text should report quantitative metrics (e.g., relative deviation, temperature range) and any uncertainty estimates on the theoretical T1.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript, the positive assessment of its significance, and the constructive comment. We address the major comment below and describe the revisions that will be made.

read point-by-point responses

  1. Referee: The computational pipeline section (following the Kubo derivation): the substitution of ML-interpolated spin-lattice coupling time series for direct ab-initio sampling is load-bearing for the NV-center T1 comparison, yet no separate validation is provided that these trajectories reproduce the phonon-resolved spectral density of the couplings at the experimental temperatures and relevant frequencies. Any systematic bias in the learned forces or matrix elements would propagate directly into the integrated correlation functions that determine the predicted T1.

    Authors: We agree that explicit validation of the spectral densities is important to rule out systematic biases in the ML trajectories. The manuscript already reports that the ML models were trained on ab initio forces and spin-lattice matrix elements, with accuracy quantified via cross-validation against held-out DFT data (Methods section). However, a direct side-by-side comparison of the phonon-resolved spectral densities of the couplings at the experimental temperatures was not presented. In the revised manuscript we will add a dedicated paragraph and supplementary figure that extracts and overlays the relevant spectral densities from (i) the long ML-driven trajectories and (ii) shorter direct ab initio MD runs performed at the same temperatures. This comparison will be restricted to the frequency window that contributes to the T1 integral, thereby confirming that the ML time series faithfully reproduce the phonon modes responsible for relaxation. We expect this addition to strengthen the computational pipeline without changing the reported T1 values or the experimental comparison. revision: yes

Circularity Check

0 steps flagged

No circularity in Kubo derivation or ML-evaluated correlation functions

full rationale

The central derivation applies standard Kubo linear-response theory to express T1 and T2 via spin-lattice coupling correlation functions, a textbook framework independent of the paper's results. Numerical values are obtained from molecular-dynamics trajectories produced by machine-learning models trained on separate ab-initio data, supplying external input to the correlation functions rather than fitting or redefining the target quantities. Experimental T1 measurements for the NV center provide an independent benchmark, with agreement reported as validation. No self-definitional mappings, fitted inputs renamed as predictions, or load-bearing self-citations appear in the chain; the pipeline remains self-contained against external ab-initio and experimental references.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on the applicability of Kubo linear-response theory to spin-lattice relaxation and on the fidelity of machine-learning potentials for generating the required correlation functions.

axioms (1)
  • domain assumption Kubo linear-response theory applies to the spin-lattice relaxation problem at the temperatures considered
    Invoked to derive the T1 and T2 expressions from correlation functions.

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