SciPost logo

SciPost Submission Page

Transient superconductivity in three-dimensional Hubbard systems by combining matrix product states and self-consistent mean-field theory

by Svenja Marten, Gunnar Bollmark, Thomas Köhler, Salvatore R. Manmana, Adrian Kantian

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Thomas Köhler
Submission information
Preprint Link: scipost_202208_00016v2  (pdf)
Date accepted: 2023-11-27
Date submitted: 2023-09-02 00:39
Submitted by: Köhler, Thomas
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
  • Quantum Physics
Approaches: Theoretical, Computational


We combine matrix-product-state (MPS) and mean-field (MF) methods to model the real-time evolution of a three-dimensional (3D) extended Hubbard system formed from one-dimensional (1D) chains arrayed in parallel with weak coupling in-between them. This approach allows us to treat much larger 3D systems of correlated fermions out-of-equilibrium over a much more extended real-time domain than previous numerical approaches. We deploy this technique to study the evolution of the system as its parameters are tuned from a charge-density wave phase into the superconducting regime, which allows us to investigate the formation of transient non-equilibrium superconductivity. In our ansatz, we use MPS solutions for chains as input for a self-consistent time-dependent MF scheme. In this way, the 3D problem is mapped onto an effective 1D Hamiltonian that allows us to use the MPS efficiently to perform the time evolution, and to measure the BCS order parameter as a function of time. Our results confirm previous findings for purely 1D systems that for such a scenario a transient superconducting state can occur.

Author comments upon resubmission

We thank the referees for their generally positive feedback. We note that the referees have highlighted the novelty of our approach with potential to yield future insight into many-body systems inside and out of equilibrium. Referee A has further commented favorably in the technical soundness of the present work and the clarity and self-contained presentation of our results. At the same time the referees have commented on some aspects of the present work and have asked for clarifications. In response, we hereby submit a revised manuscript and a diff-file which highlights the changes relative to the initially submitted manuscript. Furthermore, we respond to the queries of the referees in the present letter.

Svenja Marten, Gunnar Bollmark, Thomas Köhler, Salvatore Manmana & Adrian Kantian

List of changes

- Substantially extended the Introduction and the Conclusion
- Added more details to figure captions
- Added more details to the explanation of the eigenenergies $E_{i,α}$
- Provide more information on the degree of overestimation of the order parameter and on the possibility for independent validation of the frameworks result
- Add the value of the precision parameter ε

Published as SciPost Phys. 15, 236 (2023)

Login to report or comment