pith. sign in

arxiv: 2604.14286 · v1 · submitted 2026-04-15 · ❄️ cond-mat.str-el

Divergent spin conductivity on the verge of ferromagnetic quantum criticality

Sondre Duna Lundemo , Asle Sudb{\o} This is my paper

Pith reviewed 2026-05-10 12:19 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords spin conductivityferromagnetic quantum criticalitycritical spin fluctuationsAslamazov-Larkin analogyeasy-plane anisotropyincipient spin superfluidityWard identity
0
0 comments X

The pith

Spin conductivity diverges as a metal approaches a ferromagnetic quantum critical point due to critical spin fluctuations.

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

The paper establishes that critical spin fluctuations produce divergent corrections to the spin conductivity of a metal nearing a ferromagnetic quantum critical point. This is obtained by deriving the spin current in linear response from a Gaussian-level effective action for a system with easy-plane magnetic anisotropy. The result is framed as the spin counterpart to the Aslamazov-Larkin paraconductivity of superconductors. A sympathetic reader would care because the divergence signals enhanced spin transport and the onset of spin superfluidity in the quantum critical regime, which could appear in transport measurements on quantum critical metals.

Core claim

The spin conductivity of a metal approaching a ferromagnetic quantum critical point exhibits divergent fluctuation corrections. This effect arises from critical spin fluctuations and constitutes a spin analog of the Aslamazov-Larkin theory of paraconductivity in superconductors. The spin current is derived in linear response within a Gaussian-level treatment of the effective action for a system with easy-plane magnetic anisotropy. The theory is shown to fulfill the Ward identity and to yield vanishing spin stiffness in the normal state. The critical enhancement of the spin conductivity is interpreted as incipient spin superfluidity in the quantum critical region, further supported by an intu

What carries the argument

Gaussian-level treatment of the effective action with easy-plane magnetic anisotropy, from which the spin current is obtained in linear response to compute the fluctuation corrections.

Load-bearing premise

Fluctuations near the critical point remain perturbative so that a Gaussian treatment of the effective action suffices without higher-order corrections dominating.

What would settle it

Measurement of finite, non-divergent spin conductivity in a material tuned across a ferromagnetic quantum critical point would show the divergence claim to be incorrect.

Figures

Figures reproduced from arXiv: 2604.14286 by Asle Sudb{\o}, Sondre Duna Lundemo.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustration of two ways to approach the [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Fluctuation correction to the response kernel. Figs. (a) and (b) are the two inequivalent AL diagrams, (c) and (d) are [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
read the original abstract

We show that the spin conductivity of a metal approaching a ferromagnetic quantum critical point exhibits divergent fluctuation corrections. This effect arises from critical spin fluctuations and constitutes a spin analog of the Aslamazov-Larkin theory of paraconductivity in superconductors. The spin current is derived in linear response within a Gaussian-level treatment of the effective action for a system with easy-plane magnetic anisotropy. We demonstrate the consistency of our spin transport theory by showing that it (i) fulfills the Ward identity and (ii) yields vanishing spin stiffness in the normal state. The critical enhancement of the spin conductivity is interpreted as incipient spin superfluidity in the quantum critical region. This is further supported by an intuitive picture based on the current-loop representation of the easy-plane ferromagnet.

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 / 1 minor

Summary. The paper claims that spin conductivity in a metal near a ferromagnetic quantum critical point exhibits divergent fluctuation corrections arising from critical spin fluctuations. This is obtained via linear response within a Gaussian effective action for an easy-plane anisotropic ferromagnet and is presented as a spin analog of Aslamazov-Larkin paraconductivity. Consistency is demonstrated through fulfillment of the Ward identity and vanishing spin stiffness in the normal state, with the divergence interpreted as a signature of incipient spin superfluidity supported by a current-loop picture.

Significance. If the central result holds, the work provides a concrete transport signature of quantum critical spin fluctuations and extends the fluctuation-conductivity paradigm to the spin sector. The explicit checks that the theory satisfies the Ward identity and yields zero stiffness are valuable internal consistencies that strengthen the linear-response framework.

major comments (1)
  1. [Abstract and effective-action section] The derivation of the divergent correction rests on the Gaussian-level treatment of the effective action (abstract and the section introducing the effective action). Near the ferromagnetic QCP the Ginzburg parameter is typically O(1) or larger (especially in d=3 with Landau damping), so quartic and higher vertices generate corrections that can renormalize the propagator or cut off the divergence, as occurs in standard Hertz-Millis theory below the upper critical dimension. The Ward-identity and stiffness checks are internal to the Gaussian theory and do not address this external validity issue.
minor comments (1)
  1. [Discussion section] The intuitive current-loop representation is mentioned but not developed quantitatively; a brief comparison of its scaling with the explicit linear-response result would help readers.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive overall assessment and for the detailed major comment. We respond to it below.

read point-by-point responses

  1. Referee: [Abstract and effective-action section] The derivation of the divergent correction rests on the Gaussian-level treatment of the effective action (abstract and the section introducing the effective action). Near the ferromagnetic QCP the Ginzburg parameter is typically O(1) or larger (especially in d=3 with Landau damping), so quartic and higher vertices generate corrections that can renormalize the propagator or cut off the divergence, as occurs in standard Hertz-Millis theory below the upper critical dimension. The Ward-identity and stiffness checks are internal to the Gaussian theory and do not address this external validity issue.

    Authors: We agree that our derivation of the divergent spin conductivity is obtained within the Gaussian approximation to the effective action. This is the standard leading-order treatment for fluctuation corrections, directly analogous to the Aslamazov-Larkin calculation of paraconductivity. The Ward-identity fulfillment and vanishing spin stiffness are indeed internal consistency checks that validate the linear-response framework at this level. We acknowledge that, as the referee notes, the Ginzburg parameter is typically large near a ferromagnetic QCP (especially in d=3 with Landau damping), so that quartic and higher vertices can renormalize the propagator or cut off the divergence, consistent with the known limitations of Hertz-Millis theory below its upper critical dimension. Nevertheless, the Gaussian-level result still provides the leading divergent correction and a clear physical signature of critical spin fluctuations, which is the central message of the work. In the revised manuscript we will add a paragraph in the effective-action section (and a brief remark in the conclusions) explicitly discussing the regime of validity of the Gaussian approximation, the expected role of non-Gaussian corrections, and the qualitative robustness of the divergence as an indicator of strong fluctuation effects. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained linear response on stated Gaussian action

full rationale

The paper derives the spin conductivity correction via linear response applied to a Gaussian effective action with explicit easy-plane anisotropy. The claimed divergence follows directly from the critical propagator in that action, without any fitted parameters being relabeled as predictions, without self-citation chains supporting the central result, and without the output being definitionally identical to the input. Consistency checks (Ward identity, vanishing stiffness) are internal verifications within the same framework rather than reductions to prior results. The derivation therefore remains independent of its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The calculation rests on standard linear-response theory and Gaussian approximation to an effective bosonic action for magnetic fluctuations; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • standard math Linear response theory applies to compute spin conductivity from the effective action.
    Invoked in the derivation of spin current in linear response.
  • domain assumption Gaussian-level treatment suffices for fluctuation corrections near the critical point.
    Used for the effective action of the easy-plane ferromagnet.

pith-pipeline@v0.9.0 · 5425 in / 1263 out tokens · 31534 ms · 2026-05-10T12:19:12.213173+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

56 extracted references · 56 canonical work pages · 1 internal anchor

  1. [1]

    Sachdev,Quantum Phase Transitions, second edi- tion, 5th printing ed

    S. Sachdev,Quantum Phase Transitions, second edi- tion, 5th printing ed. (Cambridge University Press, Cam- bridge, 2015)

    work page 2015

  2. [2]

    E. C. Stoner, Collective electron specific heat and spin paramagnetism in metals, Proc. A154, 656 (1936)

    work page 1936

  3. [3]

    E. C. Stoner, Collective electron ferromagnetism, Proc. A165, 372 (1938)

    work page 1938

  4. [4]

    J. A. Hertz, Quantum critical phenomena, Phys. Rev. B 14, 1165 (1976)

    work page 1976

  5. [5]

    A. J. Millis, Effect of a nonzero temperature on quantum critical points in itinerant fermion systems, Phys. Rev. B 48, 7183 (1993)

    work page 1993

  6. [6]

    Belitz, T

    D. Belitz, T. R. Kirkpatrick, R. Narayanan, and T. Vojta, Transport Anomalies and Marginal-Fermi-Liquid Effects at a Quantum Critical Point, Phys. Rev. Lett.85, 4602 (2000)

    work page 2000

  7. [7]

    A. V. Chubukov, Self-generated locality near a ferromag- netic quantum critical point, Phys. Rev. B71, 245123 (2005)

    work page 2005

  8. [8]

    Belitz, T

    D. Belitz, T. R. Kirkpatrick, and T. Vojta, Nonanalytic behavior of the spin susceptibility in clean Fermi systems, Phys. Rev. B55, 9452 (1997)

    work page 1997

  9. [9]

    Belitz and T

    D. Belitz and T. R. Kirkpatrick, Quantum critical be- haviour of itinerant ferromagnets, J. Phys.: Condens. Matter8, 9707 (1996)

    work page 1996

  10. [10]

    Belitz, T

    D. Belitz, T. R. Kirkpatrick, and T. Vojta, First Order Transitions and Multicritical Points in Weak Itinerant Ferromagnets, Phys. Rev. Lett.82, 4707 (1999)

    work page 1999

  11. [11]

    A. V. Chubukov, C. P´ epin, and J. Rech, Instability of the Quantum-Critical Point of Itinerant Ferromagnets, Phys. Rev. Lett.92, 147003 (2004)

    work page 2004

  12. [12]

    J. Rech, C. P´ epin, and A. V. Chubukov, Quantum critical behavior in itinerant electron systems: Eliashberg theory and instability of a ferromagnetic quantum critical point, Phys. Rev. B74, 195126 (2006)

    work page 2006

  13. [13]

    Brando, D

    M. Brando, D. Belitz, F. M. Grosche, and T. R. Kirkpatrick, Metallic quantum ferromagnets, Rev. Mod. Phys.88, 025006 (2016)

    work page 2016

  14. [14]

    Z. M. Raines and A. V. Chubukov, Two-dimensional Stoner transitions beyond mean field, Phys. Rev. B110, 235433 (2024)

    work page 2024

  15. [15]

    Z. M. Raines, L. I. Glazman, and A. V. Chubukov, Un- conventional Discontinuous Transitions in Isospin Sys- tems, Phys. Rev. Lett.133, 146501 (2024)

    work page 2024

  16. [16]

    R. D. Mayrhofer, M. Schoenzeit, and A. V. Chubukov, Stoner transition at finite temperature in a two- dimensional isotropic Fermi liquid, Phys. Rev. B112, 165128 (2025)

    work page 2025

  17. [17]

    L. G. Aslamazov and A. I. Larkin, The influence of fluc- tuation pairing of electrons on the conductivity of normal metal, Physics Letters A26, 238 (1968)

    work page 1968

  18. [18]

    L. G. Aslamazov and A. I. Larkin, Effect of Fluctuations on the Properties of a Superconductor Above the Critical Temperature, Sov. Phys. Solid State10, 875 (1968)

    work page 1968

  19. [19]

    Maki, The Critical Fluctuation of the Order Param- eter in Type-II Superconductors, Prog Theor Phys39, 897 (1968)

    K. Maki, The Critical Fluctuation of the Order Param- eter in Type-II Superconductors, Prog Theor Phys39, 897 (1968)

    work page 1968

  20. [20]

    R. S. Thompson, Microwave, Flux Flow, and Fluctuation Resistance of Dirty Type-II Superconductors, Phys. Rev. B1, 327 (1970)

    work page 1970

  21. [21]

    I. Paul, C. P´ epin, B. N. Narozhny, and D. L. Maslov, Quantum Correction to Conductivity Close to a Ferro- magnetic Quantum Critical Point in Two Dimensions, Phys. Rev. Lett.95, 017206 (2005)

    work page 2005

  22. [22]

    Paul, Interaction correction of conductivity near a fer- romagnetic quantum critical point, Phys

    I. Paul, Interaction correction of conductivity near a fer- romagnetic quantum critical point, Phys. Rev. B77, 224418 (2008)

    work page 2008

  23. [23]

    G. Zala, B. N. Narozhny, and I. L. Aleiner, Interac- tion corrections at intermediate temperatures: Longitu- dinal conductivity and kinetic equation, Phys. Rev. B64, 214204 (2001)

    work page 2001

  24. [24]

    B. I. Halperin and P. C. Hohenberg, Hydrodynamic The- ory of Spin Waves, Phys. Rev.188, 898 (1969)

    work page 1969

  25. [25]

    E. B. Sonin, Analogs of superfluid currents for spins and electron-hole pairs, Sov. Phys. JETP74, 1091 (1978)

    work page 1978

  26. [26]

    E. B. Sonin, Superflows and superfluidity, Physics- Uspekhi25, 409 (1982)

    work page 1982

  27. [27]

    F. S. Nogueira and K.-H. Bennemann, Spin Josephson effect in ferromagnet/ferromagnet tunnel junctions, EPL 67, 620 (2004)

    work page 2004

  28. [28]

    Sonin, Spin currents and spin superfluidity, Advances in Physics59, 181 (2010)

    E. Sonin, Spin currents and spin superfluidity, Advances in Physics59, 181 (2010)

    work page 2010

  29. [29]

    E. B. Sonin, Spin Superfluidity, Coherent Spin Preces- sion, and Magnon BEC, J Low Temp Phys171, 757 (2013)

    work page 2013

  30. [30]

    E. B. Sonin, Spin and mass superfluidity in a ferromag- netic spin-1 Bose-Einstein condensate, Phys. Rev. B97, 224517 (2018)

    work page 2018

  31. [31]

    Y. Zhu, E. Kleinherbers, L. Levitov, and Y. Tserkovnyak, Proposal for spin superfluid quantum interference device, Phys. Rev. B112, L100405 (2025)

    work page 2025

  32. [32]

    Altland and B

    A. Altland and B. Simons,Condensed Matter Field Theory, third edition ed. (Cambridge University Press, 2023)

    work page 2023

  33. [33]

    E. I. Rashba, Spin currents in thermodynamic equilib- rium: The challenge of discerning transport currents, Phys. Rev. B68, 241315 (2003)

    work page 2003

  34. [34]

    E. B. Sonin, Equilibrium spin currents in the Rashba medium, Phys. Rev. B76, 033306 (2007)

    work page 2007

  35. [35]

    I. V. Tokatly, Equilibrium Spin Currents: Non-Abelian Gauge Invariance and Color Diamagnetism in Condensed Matter, Phys. Rev. Lett.101, 106601 (2008)

    work page 2008

  36. [36]

    Droghetti, I

    A. Droghetti, I. Rungger, A. Rubio, and I. V. Tokatly, Spin-orbit induced equilibrium spin currents in materials, Phys. Rev. B105, 024409 (2022)

    work page 2022

  37. [37]

    The sup- plemental material moreover includes Refs

    See the Supplemental material for more details. The sup- plemental material moreover includes Refs. [51–56]

    work page

  38. [38]

    S. D. Lundemo and A. Sudbø, Fluctuation conductivity in ultraclean multicomponent superconductors (2026), arXiv:2601.04308 [cond-mat]. 6

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  39. [39]

    Boyack, Restoring gauge invariance in conventional fluctuation corrections to a superconductor, Phys

    R. Boyack, Restoring gauge invariance in conventional fluctuation corrections to a superconductor, Phys. Rev. B98, 184504 (2018)

    work page 2018

  40. [40]

    Boyack, Restoring gauge invariance in conventional fluctuation corrections to a superconductor (2018), arXiv:1806.02438v2 [cond-mat]

    R. Boyack, Restoring gauge invariance in conventional fluctuation corrections to a superconductor (2018), arXiv:1806.02438v2 [cond-mat]

    work page arXiv 2018

  41. [41]

    Gindikin, S

    Y. Gindikin, S. Li, A. Levchenko, A. Kamenev, A. V. Chubukov, and D. L. Maslov, Quantum criticality and optical conductivity in a two-valley system, Phys. Rev. B110, 085139 (2024)

    work page 2024

  42. [42]

    Gindikin, D

    Y. Gindikin, D. L. Maslov, and A. V. Chubukov, Collec- tive excitations and stability of a non-Fermi liquid state near a quantum critical point of a metal, Phys. Rev. B 112, L081101 (2025)

    work page 2025

  43. [43]

    Aoyama, Spin and thermal transport and critical phenomena in three-dimensional antiferromagnets, Phys

    K. Aoyama, Spin and thermal transport and critical phenomena in three-dimensional antiferromagnets, Phys. Rev. B106, 224407 (2022)

    work page 2022

  44. [44]

    Okamoto, T

    S. Okamoto, T. Egami, and N. Nagaosa, Critical Spin Fluctuation Mechanism for the Spin Hall Effect, Phys. Rev. Lett.123, 196603 (2019)

    work page 2019

  45. [45]

    Kleinert,Multivalued Fields: In Condensed Matter, Electromagnetism, and Gravitation(WORLD SCIEN- TIFIC, 2008)

    H. Kleinert,Multivalued Fields: In Condensed Matter, Electromagnetism, and Gravitation(WORLD SCIEN- TIFIC, 2008)

    work page 2008

  46. [46]

    Larkin and A

    A. Larkin and A. Varlamov,Theory of Fluctuations in Superconductors, International Series of Monographs on Physics (Oxford University Press, Oxford, New York, 2005)

    work page 2005

  47. [47]

    Ramazashvili and P

    R. Ramazashvili and P. Coleman, Superconducting Quantum Critical Point, Phys. Rev. Lett.79, 3752 (1997)

    work page 1997

  48. [48]

    I. F. Herbut, Zero-temperatured-wave superconducting phase transition, Phys. Rev. Lett.85, 1532 (2000)

    work page 2000

  49. [49]

    V. P. Mineev and M. Sigrist, Critical fluctuation effects near the normal-metal–superconductor phase transition at low temperatures, Phys. Rev. B63, 172504 (2001)

    work page 2001

  50. [50]

    Dzero, M

    M. Dzero, M. Khodas, and A. Levchenko, Transport anomalies in multiband superconductors near the quan- tum critical point, Phys. Rev. B108, 184513 (2023)

    work page 2023

  51. [51]

    B. M. Anderson, R. Boyack, C.-T. Wu, and K. Levin, Going beyond the BCS level in the superfluid path in- tegral: A consistent treatment of electrodynamics and thermodynamics, Phys. Rev. B93, 180504 (2016)

    work page 2016

  52. [52]

    Boyack, C.-T

    R. Boyack, C.-T. Wu, B. M. Anderson, and K. Levin, Collective mode contributions to the Meissner effect: Fulde-Ferrell and pair-density wave superfluids, Phys. Rev. B95, 214501 (2017)

    work page 2017

  53. [53]

    A. J. Millis, Meissner effect in anisotropic superconduc- tors, Phys. Rev. B35, 151 (1987)

    work page 1987

  54. [54]

    Wood,The Computation of Polylogarithms, Tech

    D. Wood,The Computation of Polylogarithms, Tech. Rep. (1992)

    work page 1992

  55. [55]

    L. D. Landau and E. M. Lifshitz,Statistical Physics Part 1, 3rd ed., Course in Theoretical Physics, Vol. 5 (Perga- mon press, 1976)

    work page 1976

  56. [56]

    Divergent spin conductivity on the verge of ferromagnetic quantum criticality

    J. R. Schrieffer,Theory Of Superconductivity(Avalon Publishing, 1999). 7 Supplemental material for “Divergent spin conductivity on the verge of ferromagnetic quantum criticality” Sondre Duna Lundemo and Asle Sudbø Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway (Dated: April ...

    work page 1999