Spin order and spin excitation spectra of spin-1/2 tetramer chains
Source abstract
Abstract
Abstract We investigate the spin dynamics of a 1D spin-1/2 Heisenberg tetramer chain. Employing a combination of density matrix renormalization group, quantum renormalization group, and perturbation theory techniques, we compute the energy levels and the quantum phase diagram, analyze the phase transitions, and evaluate the dynamical structure factor (DSF), which is related to the inelastic neutron scattering (INS) spectrum and the resonant inelastic x-ray scattering (RIXS) spectrum of fractionalized and collective excitations. Our calculations suggest that the chain can transition between a hidden Z 2 × Z 2 discrete symmetry preserving tetramer phase and a Haldane phase with non-vanishing string order that breaks the hidden symmetry. These two gapped phases are intervened by an intermediate deconfined quantum critical state comprising of free spins and three-site doublets, which is a gapless critical phase with deconfined spinons that can be detected either by INS or L -edge RIXS. We find that the tetramer chain can support fractionalized (spinon) and collective (triplon and quinton) excitations. In the ferromagnetic intra-tetramer limit, the chain can support a quinton excitation which has a five-fold degenerate excited state. String order parameter calculations suggest CuInVO 5 should be in a Haldane-like phase whose INS or L -edge RIXS spectrum can support observable single-spin excitations including triplon and quinton excitations. We also identify possible two-particle excitations (two-singlon, two-triplon, triplon-quinton, and two-quinton excitations) resulting from the double spin-flip effect in the K -edge RIXS spectrum.
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Research context
OpenAlex topics: Quantum many-body systems · Physics of Superconductivity and Magnetism · Magnetism in coordination complexes
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References (65)
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1. Haldane, F. Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model. Phys. Lett. A 93, 464–468 (1983).10.1016/0375-9601(83)90631-X ↗
2. Katsura, H., Nagaosa, N. & Lee, P. A. Theory of the thermal hall effect in quantum magnets. Phys. Rev. Lett. 104, 066403 (2010).10.1103/PhysRevLett.104.066403 ↗
3. Chen, L. et al. Topological spin excitations in honeycomb ferromagnet CrI3. Phys. Rev. X 8, 041028 (2018).
4. Owerre, S. A. A first theoretical realization of honeycomb topological magnon insulator. J. Phys.: Condens. Matter 28, 386001 (2016).
5. Owerre, S. A. Topological thermal hall effect in frustrated kagome antiferromagnets. Phys. Rev. B 95, 014422 (2017).10.1103/PhysRevB.95.014422 ↗
6. Lee, K. H., Chung, S. B., Park, K. & Park, J.-G. Magnonic quantum spin hall state in the zigzag and stripe phases of the antiferromagnetic honeycomb lattice. Phys. Rev. B 97, 180401 (2018).10.1103/PhysRevB.97.180401 ↗
7. Zhang, E. Z., Chern, L. E. & Kim, Y. B. Topological magnons for thermal hall transport in frustrated magnets with bond-dependent interactions. Phys. Rev. B 103, 174402 (2021).10.1103/PhysRevB.103.174402 ↗
8. Sheikhi, B., Kargarian, M. & Langari, A. Hybrid topological magnon-phonon modes in ferromagnetic honeycomb and kagome lattices. Phys. Rev. B 104, 045139 (2021).10.1103/PhysRevB.104.045139 ↗
9. Hung, L.-Y. & Wan, Y. Ground-state degeneracy of topological phases on open surfaces. Phys. Rev. Lett. 114, 076401 (2015).10.1103/PhysRevLett.114.076401 ↗
10. Lu, T.-C., Hsieh, T. H. & Grover, T. Detecting topological order at finite temperature using entanglement negativity. Phys. Rev. Lett. 125, 116801 (2020).10.1103/PhysRevLett.125.116801 ↗
11. Wang, Z., Wu, Z. & Wang, Z. Intrinsic mixed-state topological order. PRX Quantum 6, 010314 (2025).10.1103/PRXQuantum.6.010314 ↗
12. Jafari, R. & Langari, A. Phase diagram of the one-dimensional model with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. Phys. Rev. B 76, 014412 (2007).10.1103/PhysRevB.76.014412 ↗
13. Cheng, J.-Q. et al. Fractional and composite excitations of antiferromagnetic quantum spin trimer chains. npj Quantum Mater 7, 3 (2022).10.1038/s41535-021-00416-4 ↗
14. Cheng, J.-Q., Ning, Z.-Y., Wu, H.-Q. & Yao, D.-X. Quantum phase transition and composite excitations of antiferromagnetic spin trimer chains in a magnetic field. npj Quantum Mater 9, 96 (2024).10.1038/s41535-024-00705-8 ↗
15. Prabhakar, P. S., Kumar, U., Kumar, M. & Mukherjee, A. Fractionalized excitations and resonant inelastic x-ray spectra in frustrated spin-1/2 trimer chains. Phys. Rev. B 111, 205106 (2025).10.1103/PhysRevB.111.205106 ↗
16. Li, J., Cheng, J.-Q., Datta, T. & Yao, D.-X. Resonant inelastic x-ray scattering spectra of spinon, doublon, and quarton excitations of a spin- antiferromagnetic Heisenberg trimer chain. Phys. Rev. B 111, 024404 (2025).10.1103/PhysRevB.111.024404 ↗
17. Balents, L. & Starykh, O. A. Collective spinon spin wave in a magnetized U(1) spin liquid. Phys. Rev. B 101, 020401 (2020).10.1103/PhysRevB.101.020401 ↗
18. Wang, R.-B., Keselman, A. & Starykh, O. A. Hydrodynamics of interacting spinons in the magnetized spin- chain with a uniform Dzyaloshinskii-Moriya interaction. Phys. Rev. B 105, 184429 (2022).10.1103/PhysRevB.105.184429 ↗
19. Gu, Z.-C. & Wen, X.-G. Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order. Phys. Rev. B 80, 155131 (2009).10.1103/PhysRevB.80.155131 ↗
20. Fidkowski, L. & Kitaev, A. Topological phases of fermions in one dimension. Phys. Rev. B 83, 075103 (2011).10.1103/PhysRevB.83.075103 ↗
21. Shapourian, H., Shiozaki, K. & Ryu, S. Many-body topological invariants for fermionic symmetry-protected topological phases. Phys. Rev. Lett. 118, 216402 (2017).10.1103/PhysRevLett.118.216402 ↗
22. Gong, S.-S. & Su, G. Magnetization plateaus, Haldane-like gap, string order, and hidden symmetry in a spin- tetrameric Heisenberg antiferromagnetic chain. Phys. Rev. B 78, 104416 (2008).10.1103/PhysRevB.78.104416 ↗
23. Affleck, I., Kennedy, T., Lieb, E. H. & Tasaki, H. Rigorous results on valence-bond ground states in antiferromagnets. Phys. Rev. Lett. 59, 799 (1987).10.1103/PhysRevLett.59.799 ↗
24. Scheie, A. et al. Witnessing entanglement in quantum magnets using neutron scattering. Phys. Rev. B 103, 224434 (2021).10.1103/PhysRevB.103.224434 ↗
25. White, S. R. & Affleck, I. Spectral function for the S = 1 Heisenberg antiferromagetic chain. Phys. Rev. B 77, 134437 (2008).10.1103/PhysRevB.77.134437 ↗
26. Sharma, A., Nayak, M., Rønnow, H. M. & Mila, F. Bound states and deconfined spinons in the dynamical structure factor of the J1 − J2 spin-1 chain. Phys. Rev. B 111, 064404 (2025).10.1103/PhysRevB.111.064404 ↗
27. Giamarchi, T. Quantum Physics in One Dimension (Oxford University Press, 2003). 10.1093/acprof:oso/9780198525004.001.0001.10.1093/acprof:oso/9780198525004.001.0001 ↗
28. Hakobyan, T., Hetherington, J. H. & Roger, M. Phase diagram of the frustrated two-leg ladder model. Phys. Rev. B 63, 144433 (2001).10.1103/PhysRevB.63.144433 ↗
29. Hida, K. Crossover between the Haldane-gap phase and the dimer phase in the spin-1/2 alternating Heisenberg chain. Phys. Rev. B 45, 2207 (1992).10.1103/PhysRevB.45.2207 ↗
30. Chitra, R., Pati, S., Krishnamurthy, H. R., Sen, D. & Ramasesha, S. Density-matrix renormalization-group studies of the spin-1/2 Heisenberg system with dimerization and frustration. Phys. Rev. B 52, 6581 (1995).10.1103/PhysRevB.52.6581 ↗
31. Furukawa, S., Sato, M., Onoda, S. & Furusaki, A. Ground-state phase diagram of a spin- frustrated ferromagnetic XXZ chain: Haldane dimer phase and gapped/gapless chiral phases. Phys. Rev. B 86, 094417 (2012).10.1103/PhysRevB.86.094417 ↗
32. Han, B., Tiwari, A., Hsieh, C.-T. & Ryu, S. Boundary conformal field theory and symmetry-protected topological phases in 2 + 1 dimensions. Phys. Rev. B 96, 125105 (2017).10.1103/PhysRevB.96.125105 ↗
33. Bera, A. K. et al. Emergent many-body composite excitations of interacting spin-1/2 trimers. Nat. Commun. 13, 6888 (2022).10.1038/s41467-022-34342-1 ↗
34. Li, K., Wang, J.-H., Yang, Y.-B. & Xu, Y. Symmetry-Protected Topological Phases in a Rydberg Glass. Phys. Rev. Lett. 127, 263004 (2021).10.1103/PhysRevLett.127.263004 ↗
35. Song, B. et al. Observation of symmetry-protected topological band with ultracold fermions. Sci. Adv. 4, eaao4748 (2018).10.1126/sciadv.aao4748 ↗
36. de Léséleuc, S. et al. Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms. Science 365, 775 (2019).10.1126/science.aav9105 ↗
37. Pollmann, F. & Turner, A. M. Detection of symmetry-protected topological phases in one dimension. Phys. Rev. B 86, 125441 (2012).10.1103/PhysRevB.86.125441 ↗
38. Ma, R. & Wang, C. Average Symmetry-Protected Topological Phases. Phys. Rev. X 13, 031016 (2023).
39. Gao, S. et al. Spinon continuum in the Heisenberg quantum chain compound Sr2V3O9. Phys. Rev. B 109, L020402 (2024).10.1103/PhysRevB.109.L020402 ↗
40. Nocera, A. & Alvarez, G. Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors. Phys. Rev. E 94, 053308 (2016).10.1103/PhysRevE.94.053308 ↗
41. Schlappa, J. et al. Probing multi-spinon excitations outside of the two-spinon continuum in the antiferromagnetic spin chain cuprate Sr2CuO3. Nat. Commun. 9, 5394 (2018).10.1038/s41467-018-07838-y ↗
42. Nocera, A. et al. Computing Resonant Inelastic X-Ray Scattering Spectra Using The Density Matrix Renormalization Group Method. Sci. Rep. 8, 11080 (2018).10.1038/s41598-018-29218-8 ↗
43. Kumar, U. et al. Spectroscopic signatures of next-nearest-neighbor hopping in the charge and spin dynamics of doped one-dimensional antiferromagnets. Phys. Rev. B 102, 075134 (2020).10.1103/PhysRevB.102.075134 ↗
44. Nag, A. et al. Quadrupolar magnetic excitations in an isotropic spin-1 antiferromagnet. Nat. Commun. 13, 2327 (2022).10.1038/s41467-022-30065-5 ↗
45. Schmiedinghoff, G., Múller, L., Kumar, U., Uhrig, G. S. & Fauseweh, B. Three-body bound states in antiferromagnetic spin ladders. Commun. Phys. 5, 218 (2022).10.1038/s42005-022-00986-0 ↗
46. Forte, F., Cuoco, M., Noce, C. & van den Brink, J. Doping dependence of magnetic excitations of one-dimensional cuprates as probed by resonant inelastic x-ray scattering. Phys. Rev. B 83, 245133 (2011).10.1103/PhysRevB.83.245133 ↗
47. Forte, F., Ament, L. J. P. & van den Brink, J. Magnetic excitations in La2CuO4 probed by indirect resonant inelastic x-ray scattering. Phys. Rev. B 77, 134428 (2008).10.1103/PhysRevB.77.134428 ↗
48. Ishii, K., Tsutsui, K., Kawamata, T. & Koike, Y. Observation of spin-conserving two-spinon continuum in the antiferromagnetic chain system Sr2CuO3 using Cu K-edge resonant inelastic x-ray scattering. Phys. Rev. B 112, 195132 (2025).10.1103/53wr-vpcp ↗
49. Kargarian, M., Jafari, R. & Langari, A. Renormalization of entanglement in the anisotropic Heisenberg (XXZ) model. Phys. Rev. A 77, 032346 (2008).10.1103/PhysRevA.77.032346 ↗
50. van den Brink, J. The theory of indirect resonant inelastic X-ray scattering on magnons. Europhys. Lett. 80, 47003 (2007).10.1209/0295-5075/80/47003 ↗
51. Senthil, T., Vishwanath, A., Balents, L., Sachdev, S. & Fisher, M. P. A. Deconfined quantum critical points. Science 303, 1490–1494 (2004).10.1126/science.1091806 ↗
52. Jiang, S. & Motrunich, O. Ising ferromagnet to valence bond solid transition in a one-dimensional spin chain: Analogies to deconfined quantum critical points. Phys. Rev. B 99, 075103 (2019).10.1103/PhysRevB.99.075103 ↗
53. Roberts, B., Jiang, S. & Motrunich, O. I. Deconfined quantum critical point in one dimension. Phys. Rev. B 99, 165143 (2019).10.1103/PhysRevB.99.165143 ↗
54. Huang, R.-Z., Lu, D.-C., You, Y.-Z., Meng, Z. Y. & Xiang, T. Emergent symmetry and conserved current at a one-dimensional incarnation of deconfined quantum critical point. Phys. Rev. B 100, 125137 (2019).10.1103/PhysRevB.100.125137 ↗
55. Pronk, N. T., Rivière, B. M. L. & Chepiga, N. Deconfined quantum criticality in a frustrated Haldane chain with single-ion anisotropy. Phys. Rev. B 111, L220412 (2025).10.1103/s53y-qmr4 ↗
56. Yang, S. & Xu, J.-B. Quantum entanglement and criticality in a one-dimensional deconfined quantum critical point. Phys. Rev. E 104, 064121 (2021).10.1103/PhysRevE.104.064121 ↗
57. Li, C.-X., Yang, S., Xu, J.-B. & Lin, H.-Q. Exploring dynamical quantum phase transitions in a spin model with deconfined critical point via the quantum steering ellipsoid. Phys. Rev. B 107, 085130 (2023).10.1103/PhysRevB.107.085130 ↗
58. Reja, S. & Nishimoto, S. Critical spin- tetramer compound CuInVO5: Exploring the vicinity of two multimerized singlet states. Phys. Rev. B 99, 134420 (2019).10.1103/PhysRevB.99.134420 ↗
59. Singhania, A. & Kumar, S. Cluster mean-field study of the Heisenberg model for CuInVO5. Phys. Rev. B 98, 104429 (2018).10.1103/PhysRevB.98.104429 ↗
60. Kramers, H. A. & Wannier, G. H. Statistics of the Two-Dimensional Ferromagnet. Part I. Phys. Rev. 60, 252 (1941).10.1103/PhysRev.60.252 ↗
61. Pollmann, F., Turner, A. M., Berg, E. & Oshikawa, M. Entanglement spectrum of a topological phase in one dimension. Phys. Rev. B 81, 064439 (2010).10.1103/PhysRevB.81.064439 ↗
62. Kühner, T. D. & White, S. R. Dynamical correlation functions using the density matrix renormalization group. Phys. Rev. B 60, 335 (1999).10.1103/PhysRevB.60.335 ↗
63. Jeckelmann, E. Dynamical density-matrix renormalization-group method. Phys. Rev. B 66, 045114 (2002).10.1103/PhysRevB.66.045114 ↗
64. Ummethum, J. et al. Discrete antiferromagnetic spin-wave excitations in the giant ferric wheel Fe18. Phys. Rev. B 86, 104403 (2012).10.1103/PhysRevB.86.104403 ↗
65. Hase, M., Matsumoto, M., Matsuo, A. & Kindo, K. Magnetism of the antiferromagnetic spin-1/2 tetramer compound CuInVO5. Phys. Rev. B 94, 174421 (2016).10.1103/PhysRevB.94.174421 ↗