Quasiconservation laws and suppressed transport in weakly interacting localized models
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1.
California Institute of Technology
Abstract
The stability of localization in the presence of interactions remains an open problem, with finite-size effects posing significant challenges to numerical studies. In this work, we investigate the perturbative stability of noninteracting localization under weak interactions, which allows us to analyze much larger system sizes. Focusing on disordered Anderson and quasiperiodic Aubry-André models in one dimension, and using the adiabatic gauge potential at first order in perturbation theory, we compute first-order corrections to noninteracting local integrals of motion (LIOMs). We find that for at least an 𝑂(1) fraction of the LIOMs, the corrections are well-controlled and converge at large system sizes, while others suffer from resonances. Additionally, we introduce and study the charge-transport capacity of this weakly interacting model. To first order, we find that the charge transport capacity remains bounded in the presence of interactions. Taken together, these results demonstrate that localization is perturbatively stable to weak interactions at first order, implying that, at the very least, localization persists for parametrically long times in the inverse interaction strength. We expect this perturbative stability to extend to all orders at sufficiently strong disorder, where the localization length is short, representing the true localized phase. Conversely, our findings suggest that the previously proposed interaction-induced avalanche instability, namely, in the weakly localized regime of the Anderson and Aubry-André models, is a more subtle phenomenon arising only at higher orders in perturbation theory or through nonperturbative effects.
Copyright and License
©2025 American Physical Society.
Acknowledgement
We thank Liam O'Brien, Jeanne Colbois, Wojciech De Roeck, Nicolas Laflorencie, Gil Refael, and Marko Znidaric for useful discussion. J.K.J. is supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Department of Energy Computational Science Graduate Fellowship under Award Number(s) DE-SC0025528. F.M.S. acknowledges support provided by the U.S. Department of Energy (DOE) QuantISED program through the theory consortium “Intersections of QIS and Theoretical Particle Physics” at Fermilab, and by Amazon Web Services, AWS Quantum Program. A part of this work was done at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI) of the University of Vienna. O.I.M. and J.K.J. also acknowledge support by the National Science Foundation through Grant No. DMR-2001186.
This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.
Data Availability
The data that support the findings of this article are not publicly available upon publication because it is not technically feasible and/or the cost of preparing, depositing, and hosting the data would be prohibitive within the terms of this research project. The data are available from the authors upon reasonable request.
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Additional details
Related works
- Is new version of
- Discussion Paper: arXiv:2507.03115 (arXiv)
Funding
- United States Department of Energy
- DE-SC0025528
- Amazon (United States)
- National Science Foundation
- DMR-2001186
Dates
- Accepted
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2025-10-16
Caltech Custom Metadata
- Caltech groups
- Institute for Quantum Information and Matter , Walter Burke Institute for Theoretical Physics , Division of Physics, Mathematics and Astronomy (PMA)
- Publication Status
- Published