# The Symplectic Fermi Liquid and its realization in cold atomic systems

## TL;DR

This paper develops a Fermi liquid theory for large-spin fermions with SP(N) symmetry, highlighting unique interaction effects and potential experimental realizations in cold atomic systems.

## Contribution

It introduces the Fermi liquid theory for SP(N) symmetric fermions and compares their behavior with SU(N) systems, revealing distinct interaction effects and experimental prospects.

## Key findings

- Effective mass and inverse compressibility are enhanced by interactions.
- The N-dependence of enhancements varies across regimes.
- Wilson ratio can be increased, indicating proximity to magnetic instability.

## Abstract

In this work we study a system of interacting fermions with large spin and SP(N) symmetry. We contrast their behaviour with the case of SU(N) symmetry by analysing the conserved quantities and the dynamics in each case. We also develop the Fermi liquid theory for fermions with SP(N) symmetry. We find that the effective mass and inverse compressibility are always enhanced in the presence of interactions, and that the N-dependence of the enhancement is qualitatively different in distinct parameter regimes. The Wilson ratio can be enhanced, indicating that the system can be made closer to a magnetic instability, in contrast to the SU(N) scenario. We conclude discussing what are the experimental routes to SP(N) symmetry within cold atoms and the exciting possibility to realize physics in higher dimensions in these systems.