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Unveiling the scaling laws behind spin-phonon enhanced decorrelation in spin chains

Ilija Srpak1,2, Michael J. Willatt1, Stuart C. Althorpe2, and Ali Alavi1,2,*

  • *Contact author: a.alavi@fkf.mpg.de; asa10@cam.ac.uk
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Phys. Rev. B 112, 205132 – Published 25 November, 2025

DOI: https://doi.org/10.1103/11dp-8sm4

Abstract

To study the spin-Peierls transition at finite temperatures, we use path integral molecular dynamics (PIMD) in combination with stochastic series expansion or exact diagonalization to sample the quantum Boltzmann distribution of the spin-phonon-coupled one-dimensional isotropic Heisenberg chains. The use of PIMD in this context has apparently been overlooked up to now and offers several advantages over other approaches, including no restriction on the functional forms of the phonon potential or the exchange coupling. This approach allows us to study the spin-spin correlation in such systems in detail. Looking at S=1/2, we find that it exhibits algebraic decay in the undimerized phase and exponential decay in the dimerized phase, but with many nuanced trends present. The decay exponentials in all cases roughly obey the scaling of (g2/(mωπ2))γ, where g is the spin-phonon coupling constant, m is mass, and ωπ is the frequency of the k=π phonon.

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References (41)

  1. M. Hase, I. Terasaki, and K. Uchinokura, Observation of the spin-Peierls transition in linear Cu2+ (spin-1/2) chains in an inorganic compound CuGeO3, Phys. Rev. Lett. 70, 3651 (1993).
  2. M. Weiden, R. Hauptmann, C. Geibel, F. Steglich, M. Fischer, P. Lemmens, and G. Güntherodt, Experimental evidence for a spin-Peierls-transition in α′−NaV2O5, Z. Phys. B 103, 001 (1997).
  3. I. S. Jacobs, J. W. Bray, H. R. Hart, L. V. Interrante, J. S. Kasper, G. D. Watkins, D. E. Prober, and J. C. Bonner, Spin-Peierls transitions in magnetic donor-acceptor compounds of tetrathiafulvalene (TTF) with bisdithiolene metal complexes, Phys. Rev. B 14, 3036 (1976).
  4. D. D. Thomas, H. Keller, and H. M. McConnell, Exciton magnetic resonance in Wurster's blue perchlorate, J. Chem. Phys. 39, 2321 (1963).
  5. L. D. C. Jaubert, Y. Iqbal, and H. O. Jeschke, Spin-Peierls transition in the frustrated spinels ZnCr2O4 and MgCr2O4, Phys. Rev. Lett. 134, 086702 (2025).
  6. D. B. Chesnut, Instability of a linear spin array: Application to Würster's blue perchlorate, J. Chem. Phys. 45, 4677 (1966).
  7. R. W. Kühne and U. Löw, Thermodynamical properties of a spin-12 Heisenberg chain coupled to phonons, Phys. Rev. B 60, 12125 (1999).
  8. M. Elgueta, C. Esparza, and J. Rossler, The non-adiabatic Peierls-Heisenberg model in finite clusters, J. Phys.: Condens. Matter 6, 4361 (1994).
  9. M. Routh, S. K. Saha, M. Kumar, and Z. G. Soos, Spin-Peierls transition of J1−J2 and extended models with ferromagnetic J1: Sublattice dimerization and thermodynamics of zigzag chains in β−TeVO4, Phys. Rev. B 105, 235109 (2022).
  10. R. J. Bursill, R. H. McKenzie, and C. J. Hamer, Phase diagram of a Heisenberg spin-Peierls model with quantum phonons, Phys. Rev. Lett. 83, 408 (1999).
  11. E. Orignac and R. Chitra, Mean-field theory of the spin-Peierls transition, Phys. Rev. B 70, 214436 (2004).
  12. F. Ferrari, R. Valentí, and F. Becca, Effects of spin-phonon coupling in frustrated Heisenberg models, Phys. Rev. B 104, 035126 (2021).
  13. M. Kumar, S. Ramasesha, D. Sen, and Z. G. Soos, Scaling exponents in spin-12 Heisenberg chains with dimerization and frustration studied with the density-matrix renormalization group, Phys. Rev. B 75, 052404 (2007).
  14. D. C. Johnston, R. K. Kremer, M. Troyer, X. Wang, A. Klümper, S. L. Bud'ko, A. F. Panchula, and P. C. Canfield, Thermodynamics of spin S=1/2 antiferromagnetic uniform and alternating-exchange Heisenberg chains, Phys. Rev. B 61, 9558 (2000).
  15. T. Papenbrock, T. Barnes, D. J. Dean, M. V. Stoitsov, and M. R. Strayer, Density matrix renormalization group study of critical behavior of the spin−12 alternating Heisenberg chain, Phys. Rev. B 68, 024416 (2003).
  16. F. Assaad and H. Evertz, World-line and determinantal quantum Monte Carlo methods for spins, phonons and electrons, in Computational Many-Particle Physics, edited by H. Fehske, R. Schneider, and A. Weiße (Springer, Berlin, Heidelberg, 2008), pp. 277–356.
  17. F. Michel and H. Evertz, Lattice dynamics of the Heisenberg chain coupled to finite frequency bond phonons, arXiv:0705.0799.
  18. A. Sandvik and R. Singh, Quantum Monte Carlo in the interaction representation: Application to a spin-Peierls model, Phys. Rev. B 56, 14510 (1997).
  19. H. Onishi and S. Miyashita, Temperature dependence of spin and bond ordering in a spin-Peierls system, J. Phys. Soc. Jpn. 69, 2634 (2000).
  20. D. Chandler and P. G. Wolynes, Exploiting the isomorphism between quantum theory and classical statistical mechanics of polyatomic fluids, J. Chem. Phys. 74, 4078 (1981).
  21. M. Parrinello and A. Rahman, Study of an F center in molten KCL, J. Chem. Phys 80, 860 (1984).
  22. D. M. Ceperley, Path integrals in the theory of condensed helium, Rev. Mod. Phys. 67, 279 (1995).
  23. S. Habershon, D. E. Manolopoulos, T. E. Markland, and T. F. Miller, Ring-polymer molecular dynamics: Quantum effects in chemical dynamics from classical trajectories in an extended phase space, Annu. Rev. Phys. Chem. 64, 387 (2013).
  24. T. E. Markland and M. Ceriotti, Nuclear quantum effects enter the mainstream, Nat. Rev. Chem. 2, 0109 (2018).
  25. B. Hirshberg, V. Rizzi, and M. Parrinello, Path integral molecular dynamics for bosons, Proc. Natl. Acad. Sci. USA 116, 21445 (2019).
  26. S. C. Althorpe, Path-integral approximations to quantum dynamics, Eur. Phys. J. B 94, 155 (2021).
  27. Y. Litman, V. Kapil, Y. M. Y. Feldman, D. Tisi, T. Begušić, K. Fidanyan, G. Fraux, J. Higer, M. Kellner, T. E. Li, E. S. Pós, E. Stocco, G. Trenins, B. Hirshberg, M. Rossi, and M. Ceriotti, i-PI 3.0: A flexible and efficient framework for advanced atomistic simulations, J. Chem. Phys. 161, 062504 (2024).
  28. X. Tao, P. Shushkov, and T. F. Miller, Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics, J. Chem. Phys. 148, 102327 (2018).
  29. M. Parrinello and A. Rahman, Crystal structure and pair potentials: A molecular-dynamics study, Phys. Rev. Lett. 45, 1196 (1980).
  30. A. W. Sandvik and J. Kurkijärvi, Quantum Monte Carlo simulation method for spin systems, Phys. Rev. B 43, 5950 (1991).
  31. A. W. Sandvik, Stochastic series expansion method with operator-loop update, Phys. Rev. B 59, R14157 (1999).
  32. O. F. Syljuåsen and A. W. Sandvik, Quantum Monte Carlo with directed loops, Phys. Rev. E 66, 046701 (2002).
  33. A. W. Sandvik and D. K. Campbell, Spin-Peierls transition in the Heisenberg chain with finite-frequency phonons, Phys. Rev. Lett. 83, 195 (1999).
  34. I. Najfeld and T. Havel, Derivatives of the matrix exponential and their computation, Adv. Appl. Math. 16, 321 (1995).
  35. This expression is valid in this form in the limit of P→∞, but in practice it involves smearing the operator over the exponential of the slice it acts on.
  36. J. Sato, M. Shiroishi, and M. Takahashi, Correlation functions of the spin-1/2 antiferromagnetic Heisenberg chain: Exact calculation via the generating function, Nucl. Phys. B 729, 441 (2005).
  37. W. Dobrautz, V. M. Katukuri, N. A. Bogdanov, D. Kats, G. Li Manni, and A. Alavi, Combined unitary and symmetric group approach applied to low-dimensional Heisenberg spin systems, Phys. Rev. B 105, 195123 (2022).
  38. See Supplemental Material at http://link.aps.org/supplemental/10.1103/11dp-8sm4 for convergence data and a discussion of the spin force scaling.
  39. K. Nomura and M. Yamada, Thermal Bethe-Ansatz study of the correlation length of the one-dimensional S = 1/2 Heisenberg antiferromagnet, Phys. Rev. B 43, 8217 (1991).
  40. I. Srpak, Raw data to accompany the paper “Unveiling the scaling laws behind spin-phonon enhanced decorrelation in spin chains,” Edmond, V2 (2025), https://doi.org/10.17617/3.CJINMF.
  41. H. Onishi and S. Miyashita, Quantum narrowing effect in a spin–Peierls system with quantum lattice fluctuation, J. Phys. Soc. Jpn. 72, 392 (2003).

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Phys. Rev. B 112, 205132– Published 25 November, 2025
  • Received 3 April 2025
  • Revised 17 October 2025
  • Accepted 3 November 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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