Resurgence for superconductors
Abstract
An important nonperturbative effect in quantum physics is the energy gap of superconductors, which is exponentially small in the coupling constant. A natural question is whether this effect can be incorporated in the theory of resurgence. In this paper we take some steps in this direction. We conjecture that the perturbative series for the ground state energy of a superconductor is factorially divergent, and that its leading Borel singularity is governed by the superconducting energy gap. We test this conjecture in detail in the attractive GaudinYang model, an exactly solvable model in one dimension with a BCSlike ground state. In order to do this, we develop techniques to calculate the exact perturbative series of its ground state energy up to high order. We also argue that the Borel singularity is of the renormalon type, and we identify a class of diagrams leading to factorial growth. We give additional evidence for the conjecture in other models.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 December 2019
 DOI:
 10.1088/17425468/ab4802
 arXiv:
 arXiv:1905.09569
 Bibcode:
 2019JSMTE..12.3102M
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Quantum Gases;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Superconductivity;
 Mathematical Physics
 EPrint:
 38 pages, 10 figures