Unconventional Superconductivity and Collective Excitations in Long-Range Interacting Systems

Long-range interactions are ubiquitous in nature across all scales. They are the driver behind the emergence of complex structures, from the quarks that form the atomic nucleus over the microscopic formation of solids and molecules based on atoms and ions to galaxy patterns spanning billions of light years. Modeling and predicting the emergent dynamics of many-body systems that are subject to such long-range interactions is a problem for numerical approaches, as the computational effort scales directly with the number of particles involved, making calculations for macroscopic systems intractable.

In this talk I will demonstrate, how the Bardeen–Cooper–Schrieffer (BCS) theory of superconductivity can be extended to power-law interactions using the recently developed Singular Euler–Maclaurin Expansion for lattice system [1]. We will derive a new generalized gap-equation based on the Epstein-Zeta function and discuss its efficient evaluation using a logarithmic grid and spline interpolation. I will show results for k-dependent 1D and 2D superconducting gaps, phase diagrams depending on the interaction exponent and interaction strength, and non-equilibrium Higgs oscillations that are stabilized by long-range interactions. Finally, we discuss dynamical gap transitions, that allow for a non-equilibrium identification of phase transitions.

[1] A. A. Buchheit, T. Keßler, P. K. Schuhmacher, B. Fauseweh, Exact continuum representation of long-range interacting systems, arXiv:2201.11101 (2022)