- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Relaxation toward an Ideal Chern Band through Coupling to a Markovian Bath

Bruno Mera1,2 and Tomoki Ozawa2

PDF

Phys. Rev. Lett. 137, 046601 – Published 20 July, 2026

DOI: https://doi.org/10.1103/d766-sns5

Abstract

We propose a microscopic, weak-coupling mechanism by which generic Chern bands asymptotically relax toward ideal bands. We consider coupling interacting electrons to a Caldeira-Leggett-like Ohmic bosonic bath. Using the Born-Markov approximation, we analytically show that, upon taking the leading order contribution in momentum of the form factor, Slater determinant states of a Chern band under Hartree-Fock approximation evolve toward Slater determinant states corresponding to an ideal Chern band. We also numerically validate our proposal by performing simulation of a massive Dirac model with the extended Hubbard interaction, showing that the Berry curvature and quantum metric co-evolve toward saturation of the trace condition. Our proposal provides a concrete dissipative mechanism for driving Chern bands toward ideal quantum geometry, a fundamental building block for the stabilization of fractional Chern insulators.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (30)

  1. R. Roy, Band geometry of fractional topological insulators, Phys. Rev. B 90, 165139 (2014).
  2. M. Claassen, C. H. Lee, R. Thomale, X.-L. Qi, and T. P. Devereaux, Position-momentum duality and fractional quantum Hall effect in Chern insulators, Phys. Rev. Lett. 114, 236802 (2015).
  3. T. Ozawa and B. Mera, Relations between topology and the quantum metric for Chern insulators, Phys. Rev. B 104, 045103 (2021).
  4. B. Mera and T. Ozawa, Kähler geometry and Chern insulators: Relations between topology and the quantum metric, Phys. Rev. B 104, 045104 (2021).
  5. B. Mera and T. Ozawa, Engineering geometrically flat Chern bands with Fubini-study Kähler structure, Phys. Rev. B 104, 115160 (2021).
  6. J. Wang, J. Cano, A. J. Millis, Z. Liu, and B. Yang, Exact Landau level description of geometry and interaction in a flatband, Phys. Rev. Lett. 127, 246403 (2021).
  7. P. J. Ledwith, A. Vishwanath, and D. E. Parker, Vortexability: A unifying criterion for ideal fractional Chern insulators, Phys. Rev. B 108, 205144 (2023).
  8. B. Estienne, N. Regnault, and V. Crépel, Ideal Chern bands as Landau levels in curved space, Phys. Rev. Res. 5, L032048 (2023).
  9. B. Mera and T. Ozawa, Uniqueness of Landau levels and their analogs with higher Chern numbers, Phys. Rev. Res. 6, 033238 (2024).
  10. N. Regnault and B. A. Bernevig, Fractional Chern insulator, Phys. Rev. X 1, 021014 (2011).
  11. T. Neupert, L. Santos, C. Chamon, and C. Mudry, Fractional quantum Hall states at zero magnetic field, Phys. Rev. Lett. 106, 236804 (2011).
  12. D. N. Sheng, Z.-C. Gu, K. Sun, and L. Sheng, Fractional quantum Hall effect in the absence of Landau levels, Nat. Commun. 2, 389 (2011).
  13. K. Sun, Z. Gu, H. Katsura, and S. Das Sarma, Nearly flatbands with nontrivial topology, Phys. Rev. Lett. 106, 236803 (2011).
  14. E. Tang, J.-W. Mei, and X.-G. Wen, High-temperature fractional quantum Hall states, Phys. Rev. Lett. 106, 236802 (2011).
  15. P. J. Ledwith, G. Tarnopolsky, E. Khalaf, and A. Vishwanath, Fractional Chern insulator states in twisted bilayer graphene: An analytical approach, Phys. Rev. Res. 2, 023237 (2020).
  16. J. Wang and Z. Liu, Hierarchy of ideal flatbands in chiral twisted multilayer graphene models, Phys. Rev. Lett. 128, 176403 (2022).
  17. P. J. Ledwith, A. Vishwanath, and E. Khalaf, Family of ideal Chern flatbands with arbitrary Chern number in chiral twisted graphene multilayers, Phys. Rev. Lett. 128, 176404 (2022).
  18. Z. Liu, B. Mera, M. Fujimoto, T. Ozawa, and J. Wang, Theory of generalized Landau levels and its implications for non-Abelian states, Phys. Rev. X 15, 031019 (2025).
  19. M. Fujimoto, D. E. Parker, J. Dong, E. Khalaf, A. Vishwanath, and P. Ledwith, Higher vortexability: Zero-field realization of higher Landau levels, Phys. Rev. Lett. 134, 106502 (2025).
  20. C. Paiva, J. Wang, T. Ozawa, and B. Mera, Geometrical responses of generalized Landau levels: Structure factor and the quantized Hall viscosity, Phys. Rev. B 112, 045106 (2025).
  21. Y. Onishi, A. Avdoshkin, and L. Fu, Geometric bound on the structure factor and a harmonic condition on band geometry, Phys. Rev. B 112, 035158 (2025).
  22. J. Yu, B. Lian, and S. Ryu, Wilson-loop-ideal bands and general idealization, arXiv:2509.05410.
  23. T. Fukui, Gradient flow and Bogomolny bounds for quantum metric actions, Phys. Rev. B 112, 245162 (2025).
  24. See Supplemental Material at http://link.aps.org/supplemental/10.1103/d766-sns5 for a review of mean-field theory from a geometric perspective; the Dirichlet energy functional, harmonic bands and their relation to repulsive density-density interactions; a microscopic derivation of the metriplectic flow; a discussion of the symmetry properties of the hopping matrix and the unimodular metric h; and additional numerical results comparing the exact evolution under Hartree-Fock with its small-q approximation. Supplemental Material also includes Refs. [25–27].
  25. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, United Kingdom, 2002).
  26. J. LaSalle, Some extensions of Liapunov’s second method, IRE Transactions on Circuit Theory 7, 520 (1960).
  27. T. Fukui, Y. Hatsugai, and H. Suzuki, Chern numbers in discretized Brillouin zone: Efficient method of computing (spin) Hall conductances, J. Phys. Soc. Jpn. 74, 1674 (2005).
  28. S. H. Simon and M. S. Rudner, Contrasting lattice geometry dependent versus independent quantities: Ramifications for Berry curvature, energy gaps, and dynamics, Phys. Rev. B 102, 165148 (2020).
  29. F. D. M. Haldane, Berry’s Phase and Hilbert Space Geometry as a New Ingredient in Fermi Liquid Theory, Talk presented at the Low-D Quantum Condensed Matter summer workshop, Center for Mathematical Physics, Amsterdam, Netherlands (2025).
  30. B. Mera, A. Zhang, and N. Goldman, Relating the topology of Dirac Hamiltonians to quantum geometry: When the quantum metric dictates Chern numbers and winding numbers, SciPost Phys. 12, 18 (2022).

Outline

Information

Phys. Rev. Lett. 137, 046601– Published 20 July, 2026
  • Received 14 November 2025
  • Revised 12 June 2026
  • Accepted 22 June 2026
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation