arxiv: 2605.03539 · v1 · submitted 2026-05-05 · ❄️ cond-mat.mtrl-sci · physics.comp-ph

Gauge-Field-Mediated Symmetry Breaking of Matters Under Electromagnetic Fields and Its Impact on Spin Dynamics

Uiseok Jeong , Esmaeil Taghizadeh Sisakht , Angel Rubio , Carsten A. Ullrich , Kyeong-Whan Kim , Noejung Park This is my paper

Pith reviewed 2026-05-07 16:03 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci physics.comp-ph

keywords spin-orbit couplinggauge fieldsymmetry breakingspin dynamicstime-dependent density functional theoryelectromagnetic fieldsnonequilibrium dynamicscondensed matter

0 comments p. Extension

The pith

The gauge-field term in spin-orbit coupling governs symmetry breaking and drives spin dynamics under electromagnetic fields.

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

This paper shows that when condensed matter systems are exposed to external electromagnetic fields, the gauge-field term in the spin-orbit coupling is what breaks the symmetry and allows spin dynamics to occur. Without including this term, the spins would stay frozen in states dictated by the material's symmetry, such as mirror or screw rotational symmetry. Through real-time time-dependent density functional theory calculations on representative cases, the authors find that the gauge term perturbs the canonical spin-orbit coupling, leading to gradual development of dynamical spin states over time. This holds even for weak fields, making the full gauge-invariant formulation essential for understanding nonequilibrium spin-orbit processes rather than optional.

Core claim

The central claim is that symmetry breaking and the resulting spin dynamics in materials under electromagnetic fields are controlled by the gauge-field term in the spin-orbit coupling. In the absence of this term, spins remain constrained by the system's symmetries. Real-time TDDFT simulations demonstrate that when the gauge-field term perturbs the symmetry of the canonical term, a dynamical spin state evolves during time propagation for systems with mirror, glide, and screw-rotational symmetries. The work establishes that the gauge-invariant formulation of SOC is not only formally necessary but also quantitatively important for nonequilibrium dynamics, even under weak external fields.

What carries the argument

The gauge-field term within the gauge-invariant formulation of the spin-orbit coupling operator, which perturbs symmetry in the time-dependent Hamiltonian.

If this is right

If the gauge-field term is included, spin dynamics can emerge in symmetry-constrained systems under external fields.
The canonical spin-orbit coupling term alone cannot produce the observed symmetry breaking and spin evolution.
Nonequilibrium spin-orbit dynamics require the full gauge-invariant SOC even for weak electromagnetic fields.
Materials with mirror, glide, or screw symmetries will exhibit gradual spin state development when the gauge term is active.

Where Pith is reading between the lines

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

This approach may enable optical control of spins without altering the underlying crystal symmetry.
Similar gauge-field effects could appear in other time-dependent phenomena involving relativistic corrections.
Experimental verification might involve ultrafast laser pulses on symmetric materials to observe unexpected spin precession.

Load-bearing premise

The real-time TDDFT method isolates the gauge-field effect on spin-orbit coupling from numerical errors, basis set limitations, and other parts of the Hamiltonian.

What would settle it

A calculation or experiment showing spin evolution in the absence of the gauge-field term, or no evolution when the term is included, would disprove the central role of the gauge-field term.

Figures

Figures reproduced from arXiv: 2605.03539 by Angel Rubio, Carsten A. Ullrich, Esmaeil Taghizadeh Sisakht, Kyeong-Whan Kim, Noejung Park, Uiseok Jeong.

**Figure 1.** Figure 1: FIG. 1. Mirror-reflection properties of the canonical and view at source ↗

**Figure 2.** Figure 2: FIG. 2. Symmetry breaking induced by external fields and view at source ↗

**Figure 3.** Figure 3: FIG. 3. Screw rotational symmetry of a trigonal chiral wire view at source ↗

**Figure 4.** Figure 4: FIG. 4. Influence of view at source ↗

**Figure 1.** Figure 1: FIG. 1. Spin-resolved three-dimensional band structure of the two-dimensional Rashba square-lattice model defined in Eq. (4) view at source ↗

**Figure 2.** Figure 2: FIG. 2. Crystal structure of ZrSiS viewed along the (left) top view and (right) side view, illustrating the nonsymmorphic glide view at source ↗

**Figure 3.** Figure 3: FIG. 3. Electronic band structures of Bi view at source ↗

**Figure 4.** Figure 4: FIG. 4. Real-time spin dynamics of Bi view at source ↗

**Figure 5.** Figure 5: FIG. 5. Real-time spin dynamics of ZrSiS obtained from rt-TDDFT calculations, showing all three Cartesian components of view at source ↗

read the original abstract

When a condensed-matter system is subjected to external electromagnetic fields, the gauge-invariant formulation of physical operators must explicitly incorporate the gauge-field contribution. However, in the context of spin-orbit coupling (SOC), this gauge-field term is often regarded as negligible or merely additive compared to the canonical SOC, which is typically localized near atomic cores. Here, we demonstrate that the symmetry breaking and consequent spin dynamics are governed by the gauge-field term, without which the spins remain symmetry-constrained. We perform real-time time-dependent density functional theory calculations to investigate spin-orbit dynamics, focusing on representative cases with mirror, glide, and screw-rotational symmetry. We demonstrate that when the gauge-field term in the time-dependent Hamiltonian perturbs the symmetry of the canonical term, a dynamical spin state gradually develops during the time evolution, beyond the symmetry-frozen states. We suggest that, for nonequilibrium spin-orbit dynamics, the gauge-invariant formulation of SOC is not only formally required but also quantitatively essential, even for a weak external field.

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.

Desk Editor's Note private letter to a colleague

Gauge-field term in SOC is claimed to drive symmetry breaking in TDDFT spin dynamics, but the numerics need explicit artifact checks.

read the letter

The main thing here is that the gauge-field contribution to the spin-orbit coupling is what actually breaks symmetry and lets spin dynamics develop in their real-time TDDFT runs, while the canonical term alone leaves the spins frozen by symmetry. They show this for systems with mirror, glide, and screw-rotational symmetry by comparing time evolution with and without the vector-potential-dependent part of the SOC operator. Only the full gauge-invariant version produces the gradual buildup of a dynamical spin state. That concrete demonstration in the nonequilibrium setting is the new piece, even though the formal need for gauge invariance is already in the literature they cite. The calculations follow standard TDDFT propagation and make the case that this term matters even for weak external fields, which is a useful reminder for people modeling driven spin-orbit effects. The soft spot is the numerical side. The stress-test concern holds: without reported checks that the zero-gauge-field trajectories stay strictly symmetry-constrained under the same time step, integrator, and basis, the difference could come from discretization artifacts or incomplete handling of the terms rather than the physics. If those controls are in the full manuscript they are not highlighted, and adding them would make the central claim much firmer. This is for computational condensed-matter people working on ultrafast magnetism or spintronics simulations. A reader who sets up similar TDDFT runs would get value from the caution about the gauge term. It deserves a serious referee because the point is relevant to how nonequilibrium SOC is treated and the method is straightforward to verify. Send it for peer review, but ask the referees to check the numerical validation of the symmetry constraint in the zero-gauge case.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that the gauge-field contribution to spin-orbit coupling (SOC) under external electromagnetic fields is responsible for symmetry breaking and inducing dynamical spin evolution in condensed-matter systems. Using real-time TDDFT on representative cases with mirror, glide, and screw-rotational symmetries, it shows that omitting the gauge-field term leaves spins symmetry-constrained, while its inclusion allows gradual development of spin states beyond symmetry-frozen configurations. The authors conclude that the gauge-invariant SOC formulation is formally required and quantitatively essential for nonequilibrium spin-orbit dynamics, even under weak fields.

Significance. If the central claim holds, the work would emphasize the practical importance of gauge-invariant operator formulations in real-time TDDFT for spin dynamics, with potential relevance to spintronics and magnetic materials under external fields. The real-time propagation approach provides dynamical evidence that static calculations cannot capture, and the choice of multiple symmetry classes adds generality to the demonstration.

major comments (2)

[TDDFT implementation and results] The central claim requires that symmetry breaking and spin evolution appear exclusively due to the gauge-field term in the SOC operator. The TDDFT implementation section (and associated results) must therefore include explicit verification that the zero-gauge-field trajectory remains strictly symmetry-constrained under identical numerical settings (time step, integrator, basis set, and propagation scheme) as the full-gauge case; without such checks, propagation artifacts cannot be ruled out as the source of the reported spin components.
[Abstract and results on spin dynamics] The assertion that the gauge-field term is 'quantitatively essential' even for weak fields (Abstract) is load-bearing for the practical impact. The results should therefore report quantitative measures, such as the magnitude of induced spin polarization or precession rates, with direct side-by-side comparison of the canonical-only versus gauge-inclusive Hamiltonians for at least one symmetry class.

minor comments (2)

[Title] The title contains an unusual capitalization ('Matters'); consider standardizing to 'matter' for clarity.
[Abstract] Several long sentences in the Abstract could be split or rephrased to improve readability while preserving technical content.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which highlight important aspects of rigor in our TDDFT calculations and the presentation of quantitative results. We address each major comment below and will revise the manuscript to incorporate the suggested improvements where appropriate.

read point-by-point responses

Referee: [TDDFT implementation and results] The central claim requires that symmetry breaking and spin evolution appear exclusively due to the gauge-field term in the SOC operator. The TDDFT implementation section (and associated results) must therefore include explicit verification that the zero-gauge-field trajectory remains strictly symmetry-constrained under identical numerical settings (time step, integrator, basis set, and propagation scheme) as the full-gauge case; without such checks, propagation artifacts cannot be ruled out as the source of the reported spin components.

Authors: We agree that explicit confirmation of identical numerical settings is necessary to exclude propagation artifacts and support the central claim. In our study, the zero-gauge-field and gauge-inclusive calculations were performed using precisely the same time step, integrator, basis set, and propagation scheme, as described in the Computational Methods section. The presented results for the representative symmetries demonstrate that the zero-gauge-field trajectories remain strictly symmetry-constrained, with spin components staying at zero (within the symmetry of the canonical SOC term). To make this verification fully explicit, we will add a dedicated statement in the TDDFT implementation section confirming the shared numerical parameters and noting that no symmetry-breaking spin components develop in the zero-gauge case. This revision will be included in the updated manuscript. revision: yes
Referee: [Abstract and results on spin dynamics] The assertion that the gauge-field term is 'quantitatively essential' even for weak fields (Abstract) is load-bearing for the practical impact. The results should therefore report quantitative measures, such as the magnitude of induced spin polarization or precession rates, with direct side-by-side comparison of the canonical-only versus gauge-inclusive Hamiltonians for at least one symmetry class.

Authors: We acknowledge that adding quantitative measures would strengthen the claim of quantitative essentiality for weak fields. Although the manuscript focuses on the qualitative emergence of spin dynamics due to the gauge-field term, we will revise the Results section to include direct side-by-side comparisons for at least one symmetry class (e.g., the mirror symmetry case). This will report the magnitude of induced spin polarization and the associated timescales, contrasting the canonical-only Hamiltonian (which remains symmetry-constrained) with the gauge-inclusive case. The updated manuscript will incorporate these quantitative details to better support the Abstract statement. revision: yes

Circularity Check

0 steps flagged

No circularity: TDDFT symmetry-breaking result is a direct numerical comparison, not a self-referential fit or definition

full rationale

The paper's core demonstration rests on real-time TDDFT propagations that explicitly compare the time-dependent Hamiltonian with and without the gauge-field contribution to the SOC operator. The observed emergence of spin components when the gauge term is retained is an output of the propagation under the stated numerical settings, not presupposed by redefining the input or by fitting parameters to the target observable. No equations reduce the reported spin dynamics to a fitted quantity by construction, and no load-bearing uniqueness theorem or ansatz is imported via self-citation in a way that collapses the claim. The separation of gauge versus canonical terms is implemented at the level of the Hamiltonian before propagation, making the symmetry-breaking result falsifiable against the zero-gauge reference trajectory rather than tautological.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit list of free parameters, axioms, or invented entities; TDDFT itself rests on standard approximations whose details are not supplied.

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