Non-ergodic one-magnon magnetization dynamics of the Kagome lattice antiferromagnet
-
Henrik Schlüter
und
Jannis Eckseler
Abstract
The present view of modern physics on non-equilibrium dynamics is that generic systems equilibrate or thermalize under rather general conditions, even closed systems under unitary time evolution. The investigation of exceptions thus not only appears attractive, in view of quantum computing where thermalization is a threat it also seems to be necessary. Here, we present aspects of the one-magnon dynamics on the Kagome lattice antiferromagnet as an example of a non-equilibrating dynamics due to flat bands. Similar to the one-dimensional delta chain localized eigenstates also called localized magnons lead to disorder-free localization and prevent the system from equilibration.
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: 355031190 (FOR 2692)
Award Identifier / Grant number: 397300368 (SCHN 615/25-2)
Award Identifier / Grant number: 449703145 (SCHN 615/28-1)
Acknowledgments
We would like to thank our collaborator and friend Johannes Richter, who passed away in May 2025, for many insightful discussions. HS likes to thank Katarína Karl’ová for inspiring discussions. This work was supported by the Deutsche Forschungsgemeinschaft DFG (355031190 (FOR 2692); 397300368 (SCHN 615/25-2)) as well as (449703145 (SCHN 615/28-1)).
-
Research ethics: Not applicable.
-
Informed consent: Not applicable.
-
Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
-
Use of Large Language Models, AI and Machine Learning Tools: None declared.
-
Conflict of interest: The author states no conflict of interest.
-
Research funding: This work was supported by the Deutsche Forschungsgemeinschaft DFG (355031190 (FOR 2692); 397300368 (SCHN 615/25-2)) as well as (449703145 (SCHN 615/28-1)).
-
Data availability: Not applicable.
References
[1] J. M. Deutsch, “Quantum statistical mechanics in a closed system,” Phys. Rev. A, vol. 43, no. 4, p. 2046, 1991, https://doi.org/10.1103/physreva.43.2046.Suche in Google Scholar PubMed
[2] M. Srednicki, “Chaos and quantum thermalization,” Phys. Rev. E, vol. 50, no. 2, p. 888, 1994, https://doi.org/10.1103/physreve.50.888.Suche in Google Scholar PubMed
[3] J. Schnack and H. Feldmeier, “Statistical properties of fermionic molecular dynamics,” Nucl. Phys. A, vol. 601, no. 2, p. 181, 1996, https://doi.org/10.1016/0375-9474(95)00505-6.Suche in Google Scholar
[4] H. Tasaki, “From quantum dynamics to the canonical distribution: General picture and a rigorous example,” Phys. Rev. Lett., vol. 80, no. 7, p. 1373, 1998, https://doi.org/10.1103/physrevlett.80.1373.Suche in Google Scholar
[5] M. Rigol, V. Dunjko, and M. Olshanii, “Thermalization and its mechanism for generic isolated quantum systems,” Nature, vol. 452, p. 854, 2008, https://doi.org/10.1038/nature06838.Suche in Google Scholar PubMed
[6] A. Polkovnikov, K. Sengupta, A. Silva, and M. Vengalattore, “Colloquium,” Rev. Mod. Phys., vol. 83, no. 3, p. 863, 2011, https://doi.org/10.1103/revmodphys.83.863.Suche in Google Scholar
[7] P. Reimann and M. Kastner, “Equilibration of isolated macroscopic quantum systems,” N. J. Phys., vol. 14, no. 4, p. 043020, 2012, https://doi.org/10.1088/1367-2630/14/4/043020.Suche in Google Scholar
[8] R. Steinigeweg, A. Khodja, H. Niemeyer, C. Gogolin, and J. Gemmer, “Pushing the limits of the eigenstate thermalization hypothesis towards mesoscopic quantum systems,” Phys. Rev. Lett., vol. 112, no. 13, p. 130403, 2014, https://doi.org/10.1103/physrevlett.112.130403.Suche in Google Scholar PubMed
[9] C. Gogolin and J. Eisert, “Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems,” Rep. Prog. Phys., vol. 79, no. 5, p. 056001, 2016, https://doi.org/10.1088/0034-4885/79/5/056001.Suche in Google Scholar PubMed
[10] L. D’Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol, “From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics,” Adv. Phys., vol. 65, no. 3, p. 239, 2016, https://doi.org/10.1080/00018732.2016.1198134.Suche in Google Scholar
[11] F. Borgonovi, F. M. Izrailev, L. F. Santos, and V. G. Zelevinsky, “Quantum chaos and thermalization in isolated systems of interacting particles,” Phys. Rep., vol. 626, p. 1, 2016, https://doi.org/10.1016/j.physrep.2016.02.005.Suche in Google Scholar
[12] Y.-L. Wu, D.-L. Deng, X. Li, and S. Das Sarma, “Intrinsic decoherence in isolated quantum systems,” Phys. Rev. B, vol. 95, no. 1, p. 014202, 2017, https://doi.org/10.1103/physrevb.95.014202.Suche in Google Scholar
[13] L. Vidmar and M. Rigol, “Generalized gibbs ensemble in integrable lattice models,” J. Stat. Mech.: Theo. Exp., vol. 2016, no. 6, p. 064007, 2016, https://doi.org/10.1088/1742-5468/2016/06/064007.Suche in Google Scholar
[14] F. Johannesmann, J. Eckseler, H. Schlüter, and J. Schnack, “Nonergodic one-magnon magnetization dynamics of the antiferromagnetic delta chain,” Phys. Rev. B, vol. 108, no. 6, p. 064304, 2023, https://doi.org/10.1103/physrevb.108.064304.Suche in Google Scholar
[15] A. Mielke and H. Tasaki, “Ferromagnetism in the Hubbard-model – examples from models with degenerate single-electron ground-states,” Commun. Math. Phys., vol. 158, p. 341, 1993, https://doi.org/10.1007/bf02108079.Suche in Google Scholar
[16] J. Schnack, H.-J. Schmidt, J. Richter, and J. Schulenburg, “Independent magnon states on magnetic polytopes,” Eur. Phys. J. B, vol. 24, no. i, p. 475, 2001, https://doi.org/10.1007/s10051-001-8701-6.Suche in Google Scholar
[17] J. Schulenburg, A. Honecker, J. Schnack, J. Richter, and H.-J. Schmidt, “Macroscopic magnetization jumps due to independent magnons in frustrated quantum spin lattices,” Phys. Rev. Lett., vol. 88, no. 16, p. 167207, 2002, https://doi.org/10.1103/physrevlett.88.167207.Suche in Google Scholar
[18] S. A. Blundell and M. D. Núñez-Regueiro, “Quantum topological excitations: From the sawtooth lattice to the Heisenberg chain,” Eur. Phys. J. B, vol. 31, p. 453, 2003, https://doi.org/10.1140/epjb/e2003-00054-2.Suche in Google Scholar
[19] J. Richter, J. Schulenburg, A. Honecker, J. Schnack, and H.-J. Schmidt, “Exact eigenstates and macroscopic magnetization jumps in strongly frustrated spin lattices,” J. Phys.: Condens. Matter, vol. 16, p. S779, 2004, https://doi.org/10.1088/0953-8984/16/11/029.Suche in Google Scholar
[20] H.-J. Schmidt, J. Richter, and R. Moessner, “Linear independence of localized magnon states,” J. Phys. A: Math. Gen., vol. 39, no. 34, p. 10673, 2006, https://doi.org/10.1088/0305-4470/39/34/006.Suche in Google Scholar
[21] M. E. Zhitomirsky and H. Tsunetsugu, “Exact low-temperature behavior of a kagomé antiferromagnet at high fields,” Phys. Rev. B, vol. 70, no. 10, p. 100403(R), 2004, https://doi.org/10.1103/physrevb.70.100403.Suche in Google Scholar
[22] O. Derzhko, J. Richter, A. Honecker, M. Maksymenko, and R. Moessner, “Low-temperature properties of the Hubbard model on highly frustrated one-dimensional lattices,” Phys. Rev. B, vol. 81, no. 1, p. 014421, 2010, https://doi.org/10.1103/physrevb.81.014421.Suche in Google Scholar
[23] M. Maksymenko, A. Honecker, R. Moessner, J. Richter, and O. Derzhko, “Flat-band ferromagnetism as a Pauli-correlated percolation problem,” Phys. Rev. Lett., vol. 109, no. 9, p. 096404, 2012, https://doi.org/10.1103/physrevlett.109.096404.Suche in Google Scholar PubMed
[24] O. Derzhko, J. Richter, and M. Maksymenko, “Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons,” Int. J. Mod. Phys. B, vol. 29, no. 12, p. 1530007, 2015, https://doi.org/10.1142/s0217979215300078.Suche in Google Scholar
[25] D. Leykam, A. Andreanov, and S. Flach, “Artificial flat band systems: from lattice models to experiments,” Adv. Phys.: X, vol. 3, no. 1, p. 1473052, 2018, https://doi.org/10.1080/23746149.2018.1473052.Suche in Google Scholar
[26] S. Tilleke, M. Daumann, and T. Dahm, “Nearest neighbour particle-particle interaction in fermionic quasi one-dimensional flat band lattices,” Z. Naturforsch. A, vol. 75, no. 5, p. 393, 2020, https://doi.org/10.1515/zna-2019-0371.Suche in Google Scholar
[27] J. Richter, V. Ohanyan, J. Schulenburg, and J. Schnack, “Electric field driven flat bands: Enhanced magnetoelectric and electrocaloric effects in frustrated quantum magnets,” Phys. Rev. B, vol. 105, no. 5, p. 054420, 2022, https://doi.org/10.1103/physrevb.105.054420.Suche in Google Scholar
[28] P. A. McClarty, M. Haque, A. Sen, and J. Richter, “Disorder-free localization and many-body quantum scars from magnetic frustration,” Phys. Rev. B, vol. 102, no. 15, p. 224303, 2020, https://doi.org/10.1103/physrevb.102.224303.Suche in Google Scholar
[29] J. Schnack, J. Schulenburg, A. Honecker, and J. Richter, “Magnon crystallization in the kagome lattice antiferromagnet,” Phys. Rev. Lett., vol. 125, no. 11, p. 117207, 2020, https://doi.org/10.1103/physrevlett.125.117207.Suche in Google Scholar
[30] H. Schlüter, “Zu dynamischen und thermodynamischen Eigenschaften frustrierter Spinsysteme mit flachen Energiebändern,” Ph.D. thesis, Bielefeld University, Faculty of Physics, Bielefeld, 2024.Suche in Google Scholar
[31] G. Fischer, Lineare Algebra: Eine Einführung für Studienanfänger, Grundkurs Mathematik, Wiesbaden, Springer Fachmedien Wiesbaden, 2013.Suche in Google Scholar
[32] J. Eckseler and J. Schnack, “Permanent oscillations and solitary wave behavior in flatband Heisenberg quantum spin systems,” Phys. Rev. Res., vol. 7, no. 1, p. 013178, 2025, https://doi.org/10.1103/physrevresearch.7.013178.Suche in Google Scholar
[33] D. Yaremchuk, et al.., “Frustrated kagome-lattice bilayer quantum Heisenberg antiferromagnet,” Phys. Rev. B, vol. 112, no. 17, p. 024402, 2025, https://doi.org/10.1103/1rzb-s69p.Suche in Google Scholar
[34] A. Mielke, “Ferromagnetism in the Hubbard model on line graphs and further considerations,” J. Phys. A: Math. Gen., vol. 24, no. 14, p. 3311, 1991, https://doi.org/10.1088/0305-4470/24/14/018.Suche in Google Scholar
[35] A. Mielke, “Ferromagnetic ground states for the Hubbard model on line graphs,” J. Phys. A: Math. Gen., vol. 24, no. 2, p. L73, 1991, https://doi.org/10.1088/0305-4470/24/2/005.Suche in Google Scholar
[36] A. Mielke, “Exact ground-states for the Hubbard-model on the kagome lattice,” J. Phys. A-Math. Gen., vol. 25, no. 16, p. 4335, 1992, https://doi.org/10.1088/0305-4470/25/16/011.Suche in Google Scholar
[37] H. Tasaki, “Ferromagnetism in the Hubbard models with degenerate single-electron ground states,” Phys. Rev. Lett., vol. 69, no. 10, p. 1608, 1992, https://doi.org/10.1103/physrevlett.69.1608.Suche in Google Scholar
[38] A. Giesekus and U. Brandt, “Low-energy states for correlated-electron models in the strong-coupling limit,” Phys. Rev. B, vol. 53, no. 3, p. 1635, 1996, https://doi.org/10.1103/physrevb.53.1635.Suche in Google Scholar PubMed
[39] H. Tasaki, “From Nagaoka’s ferromagnetism to flat-band ferromagnetism and beyond – an introduction to ferromagnetism in the Hubbard model,” Prog. Theor. Phys., vol. 99, no. 4, p. 489, 1998, https://doi.org/10.1143/ptp.99.489.Suche in Google Scholar
[40] E. J. Bergholtz and Z. Liu, “Toplogical flat band models and fractional Chern insulators,” Int. J. Mod. Phys. B, vol. 27, no. 24, p. 1330017, 2013, https://doi.org/10.1142/s021797921330017x.Suche in Google Scholar
[41] M. Maksymenko, R. Moessner, and K. Shtengel, “Persistence of the flat band in a kagome magnet with dipolar interactions,” Phys. Rev. B, vol. 96, no. 13, p. 134411, 2017, https://doi.org/10.1103/physrevb.96.134411.Suche in Google Scholar
[42] M. Daumann and T. Dahm, “Anomalous diffusion, prethermalization, and particle binding in an interacting flat band system,” N. J. Phys., vol. 26, no. 6, p. 063001, 2024, https://doi.org/10.1088/1367-2630/ad4e5d.Suche in Google Scholar
[43] M. Kawano, F. Pollmann, and M. Knap, “Unconventional spin transport in strongly correlated kagome systems,” Phys. Rev. B, vol. 109, no. 12, p. L121111, 2024, https://doi.org/10.1103/physrevb.109.l121111.Suche in Google Scholar
© 2025 Walter de Gruyter GmbH, Berlin/Boston
