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Symmetry breaking and thermal phase transition of the spin-1 quantum magnet with SU(3) symmetry on the simple cubic lattice

Nils Caci1, Dominik Chudy2, Pablo Daniel Mendez Mariscal2, Daniel Ueltschi3, and Stefan Wessel2

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Phys. Rev. B 112, 165114 – Published 10 October, 2025

DOI: https://doi.org/10.1103/w7fl-yy4x

Abstract

Using a combined analysis from Poisson-Dirichlet and symmetry-breaking calculations as well as quantum Monte Carlo simulations, we examine the ordered phase and the thermal phase transition of the three-dimensional spin-1 quantum magnet on the simple cubic lattice with bilinear and biquadratic interactions and SU(3) internal symmetry. We obtain exact results for the order parameter distribution function that compare well to the quantum Monte Carlo data. Furthermore, based on a detailed finite-size analysis, we provide evidence that the thermal melting transition at the SU(3) point is either weakly first order in this system or, if continuous, it falls beyond the unitarity bounds of conformal field theory.

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References (44)

  1. D. B. Kaplan, J.-W. Lee, D. T. Son, and M. A. Stephanov, Conformality lost, Phys. Rev. D 80, 125005 (2009).
  2. A. Nahum, J. T. Chalker, P. Serna, M. Ortuño, and A. M. Somoza, Deconfined quantum criticality, scaling violations, and classical loop models, Phys. Rev. X 5, 041048 (2015).
  3. C. Wang, A. Nahum, M. A. Metlitski, C. Xu, and T. Senthil, Deconfined quantum critical points: Symmetries and dualities, Phys. Rev. X 7, 031051 (2017).
  4. V. Gorbenko, S. Rychkov, and B. Zan, Walking, weak first-order transitions, and complex CFTs, J. High Energy Phys. 10 (2018) 108.
  5. V. Gorbenko, S. Rychkov, and B. Zan, Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at Q>4, SciPost Phys. 5, 050 (2018).
  6. H. Ma and Y.-C. He, Shadow of complex fixed point: Approximate conformality of q≥4 Potts model, Phys. Rev. B 99, 195130 (2019).
  7. F. S. Nogueira, J. van den Brink, and A. Sudbø, Conformality loss and quantum criticality in topological Higgs electrodynamics in 2+1 dimensions, Phys. Rev. D 100, 085005 (2019).
  8. S. Iino, S. Morita, N. Kawashima, and A. W. Sandvik, Detecting signals of weakly first-order phase transitions in two-dimensional Potts models, J. Phys. Soc. Jpn. 88, 034006 (2019).
  9. J. D'Emidio, A. A. Eberharter, and A. M. Läuchli, Diagnosing weakly first-order phase transitions by coupling to order parameters, SciPost Phys. 15, 061 (2023).
  10. N. Caci, P. Mühlbacher, D. Ueltschi, and S. Wessel, Poisson-Dirichlet distributions and weakly first-order spin-nematic phase transitions, Phys. Rev. B 107, L020409 (2023).
  11. K. Tanaka, A. Tanaka, and T. Idogaki, Long-range order in the ground state of the s=1 isotropic bilinear-biquadratic exchange Hamiltonian, J. Phys. A: Math. Gen. 34, 8767 (2001).
  12. K. Harada and N. Kawashima, Quadrupolar order in isotropic Heisenberg models with biquadratic interaction, Phys. Rev. B 65, 052403 (2002).
  13. C. D. Batista and G. Ortiz, Algebraic approach to interacting quantum systems, Adv. Phys. 53, 1 (2004).
  14. T. A. Tóth, A. M. Läuchli, F. Mila, and K. Penc, Competition between two- and three-sublattice ordering for s=1 spins on the square lattice, Phys. Rev. B 85, 140403(R) (2012).
  15. Yu.A. Fridman, O. A. Kosmachev, and Ph. N. Klevets, Spin nematic and orthogonal nematic states in S=1 non-Heisenberg magnet, J. Magn. Magn. Mater. 325, 125 (2013).
  16. D. Ueltschi, Ferromagnetism, antiferromagnetism, and the curious nematic phase of S=1 quantum spin systems, Phys. Rev. E 91, 042132 (2015).
  17. J. E. Björnberg, J. Fröhlich, and D. Ueltschi, Quantum spins and random loops on the complete graph, Commun. Math. Phys. 375, 1629 (2020).
  18. B. Tóth, Improved lower bound on the thermodynamic pressure of the spin 1/2 Heisenberg ferromagnet, Lett. Math. Phys. 28, 75 (1993).
  19. M. Aizenman and B. Nachtergaele, Geometric aspects of quantum spin states, Commun. Math. Phys. 164, 17 (1994).
  20. D. Ueltschi, Random loop representations for quantum spin systems, J. Math. Phys. 54, 083301 (2013).
  21. C. Goldschmidt, D. Ueltschi, and P. Windridge, Quantum Heisenberg models and their probabilistic representations, in Entropy and the Quantum II, Contemp. Math. Vol. 552 (American Mathematical Society, 2011), pp. 177–224.
  22. S. Grosskinsky, A. A. Lovisolo, and D. Ueltschi, Lattice permutations and Poisson-Dirichlet distribution of cycle lengths, J. Stat. Phys. 146, 1105 (2012).
  23. A. Nahum, J. T. Chalker, P. Serna, M. Ortuño, and A. M. Somoza, Length distributions in loop soups, Phys. Rev. Lett. 111, 100601 (2013).
  24. D. Ueltschi, Universal behaviour of 3D loop soup models, in 6th Warsaw School of Statistical Physics, edited by B. Cichocki, M. Napiorkowski, J. Piasecki, and P. Szymczak (Warsaw University Press, Warsaw, 2017), pp. 65–100.
  25. S. Rychkov, EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions, Springer Briefs in Physics (Springer, Cham, 2017).
  26. A. Pelissetto and E. Vicari, Three-dimensional ferromagnetic CPN−1 models, Phys. Rev. E 100, 022122 (2019).
  27. N. Read and S. Sachdev, Spin-Peierls, valence-bond solid, and Néel ground states of low-dimensional quantum antiferromagnets, Phys. Rev. B 42, 4568 (1990).
  28. N. Caci, D. Chudy, P. D. Mendez Mariscal, D. Ueltschi, and S. Wessel, Figure data to “Symmetry breaking and thermal phase transition of the spin-1 quantum magnet with SU(3) symmetry on the simple cubic lattice, https://zenodo.org/records/15226306 (2025).
  29. D. Ruelle, Statistical Mechanics (W.A. Benjamin, London, 1969).
  30. R. B. Israel, Convexity in the Theory of Lattice Gases (Princeton University Press, Princeton, 2016).
  31. C. Itzykson and J.-B. Zuber, The planar approximation. II, J. Math. Phys. 21, 411 (1980).
  32. A. W. Sandvik and J. Kurkijärvi, Quantum Monte Carlo simulation method for spin systems, Phys. Rev. B 43, 5950 (1991).
  33. A. W. Sandvik, Stochastic series expansion method with operator-loop update, Phys. Rev. B 59, R14157 (1999).
  34. O. F. Syljuåsen and A. W. Sandvik, Quantum Monte Carlo with directed loops, Phys. Rev. E 66, 046701 (2002).
  35. F. Alet, S. Wessel, and M. Troyer, Generalized directed loop method for quantum Monte Carlo simulations, Phys. Rev. E 71, 036706 (2005).
  36. H. Nagata, M. Žukovič, and T. Idogaki, Monte Carlo simulation of the three-dimensional XY model with bilinear– biquadratic exchange interaction, J. Magn. Magn. Mater. 234, 320 (2001).
  37. M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, Critical behavior of the three-dimensional XY universality class, Phys. Rev. B 63, 214503 (2001).
  38. V. Privman and M. E. Fisher, Finite-size effects at first-order transitions, in Finite-Size Scaling (Elsevier, Amsterdam, 1988), pp. 149–181.
  39. W. Janke, Accurate first-order transition points from finite-size data without power-law corrections, Phys. Rev. B 47, 14757 (1993).
  40. J. Lee and J. M. Kosterlitz, New numerical method to study phase transitions, Phys. Rev. Lett. 65, 137 (1990).
  41. J. Lee and J. M. Kosterlitz, Finite-size scaling and Monte Carlo simulations of first-order phase transitions, Phys. Rev. B 43, 3265 (1991).
  42. F. Y. Wu, The Potts model, Rev. Mod. Phys. 54, 235 (1982).
  43. E. Buddenoir and S. Wallon, The correlation length of the Potts model at the first-order transition point, J. Phys. A: Math. Gen. 26, 3045 (1993).
  44. J. Kent-Dobias and J. P. Sethna, Cluster representations and the Wolff algorithm in arbitrary external fields, Phys. Rev. E 98, 063306 (2018).

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Phys. Rev. B 112, 165114– Published 10 October, 2025
  • Received 5 June 2025
  • Revised 22 September 2025
  • Accepted 25 September 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.

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