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Bootstrapping Flatband Superconductors: Rigorous Lower Bounds on Superfluid Stiffness
Qiang Gao1, Zhaoyu Han1, Eslam Khalaf1
1Harvard University, Department of Physics, Cambridge, Massachusetts 02138, USA.
Physical Review Letters
|March 6, 2026
Summary
This study introduces the quantum many-body bootstrap to bound superfluid stiffness in superconductors. The method provides rigorous lower bounds, aiding the study of strongly coupled systems.
Area of Science:
- Condensed Matter Physics
- Quantum Many-Body Theory
Background:
- Superfluid stiffness is crucial for superconductor transition temperatures, particularly in strongly coupled regimes.
- Accurately calculating this quantum many-body property in microscopic models is challenging.
Purpose of the Study:
- To demonstrate the utility of the quantum many-body bootstrap, specifically the reduced density matrix (RDM) bootstrap, for deriving rigorous lower bounds on superfluid stiffness.
- To apply this framework to frustration-free interacting models with superconducting ground states.
Main Methods:
- Utilized the quantum many-body bootstrap framework, focusing on the reduced density matrix (RDM) bootstrap.
- Numerically applied the method to quantum geometric nesting models, a class of frustration-free models relevant to flatband superconductivity.
Main Results:
- Obtained rigorous lower bounds on superfluid stiffness in specific models.
- Discovered a general relationship between stiffness and pair mass in flatband superconductors.
- Showed that additional interactions, like magnetic couplings, can enhance superfluid stiffness beyond the standard Hubbard model.
Conclusions:
- The quantum many-body bootstrap is a powerful tool for deriving rigorous bounds on physical quantities in many-body systems.
- The RDM bootstrap offers a viable approach to study superfluid stiffness and related properties in complex superconducting models.
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