Non-Hermitian Fermi-Dirac Distribution in Persistent Current Transport

This repository contains the code developed to accompany the Letter titled Non-Hermitian Fermi-Dirac Distribution in Persistent Current Transport [1].

Contents

• SNS.ipynb: A phase-biased superconducting-normal-superconducting (SNS) junction.
• Ring.ipynb: A normal metallic ring threaded by a magnetic flux.
• NonHermitianFermiDiracPersistentCurrent.nb: Mathematica notebook (view online) for symbolic derivation of the non-Hermitian Fermi-Dirac distribution and relevant analytical calculations.

Usage

To run the Jupyter notebooks, ensure you have DMRGpy installed. Each notebook is self-contained and provides step-by-step computation leading to the ground state energy and persistent current as a function of the phase. The analysis focuses on the influence of many-body interactions on the persistent currents and scrutinizes the signatures of exceptional points within these systems.

For the Mathematica notebook, we demonstrate the symbolic derivation of our formalism, including:

• Derivation and visualization of the non-Hermitian Fermi-Dirac distribution.
• Continuity of the persistent current at exceptional points, as discussed in the blog titled Quantum many-body observables in equilibrium are continuous at exceptional points.
• Analytical expressions and and numerical verifications for Green's function.

This notebook has been featured in the Wolfram Community in the editorial columns: Staff Picks and Publication Materials.

Reference

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[1] P.-X. Shen, Z. Lu, J. L. Lado, and M. Trif, Non-Hermitian Fermi-Dirac Distribution in Persistent Current Transport, Phys. Rev. Lett. 133, 086301 (2024).

Please note that in the final published version of our Letter, there is a minor typo in the sentence located in the lower left corner of page 2: "For isolated and Hermitian systems $\mathcal{H}_\mathrm{sys}$, the persistent current $I_\mathrm{iso}(\phi)$ n the many-body ground state with energy $E_0$ follows [56]," where the word n should be in.

Citation

If you use this code or notebook in your research, please cite our Letter:

@article{Shen2024NonHermitian,
  title = {Non-{{Hermitian Fermi-Dirac Distribution}} in {{Persistent Current Transport}}},
  author = {Shen, Pei-Xin and Lu, Zhide and Lado, Jose L. and Trif, Mircea},
  year = {2024},
  month = aug,
  volume = {133},
  number = {8},
  pages = {086301},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.133.086301},
  journal = {Physical Review Letters}
}

Funding

This work is supported by the Foundation for Polish Science project MagTop (No. FENG.02.01-IP.05-0028/23) co-financed by the European Union from the funds of Priority 2 of the European Funds for a Smart Economy Program 2021–2027 (FENG) and by the National Science Centre (Poland) OPUS Grant No. 2021/41/B/ST3/04475. P.-X. S. and Z. L. acknowledge support from the Tsinghua University Dushi Program and Shanghai Qi Zhi Institute. J. L. L. acknowledges the computational resources provided by the Aalto Science-IT project the financial support from the Academy of Finland Projects No. 331342 and No. 358088. P.-X. S. acknowledges additional support from the European Union’s Horizon Europe research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101180589 (SymPhysAI).