# Solvable Strong-coupling Quantum Dot Model with a Non-Fermi-liquid Pairing Transition

## TL;DR

This paper introduces the Yukawa-SYK model, a solvable random interacting quantum dot system exhibiting non-Fermi liquid behavior and a Kosterlitz-Thouless quantum-critical pairing transition, controlled by large-$M$, large-$N$ limits.

## Contribution

It presents a solvable model with exotic pairing and non-Fermi liquid phases, revealing conditions for pairing and critical behavior in strongly interacting quantum dots.

## Key findings

- Pairing occurs only in specific regions of the (M,N) parameter space.
- Fermion incoherence can prevent Cooper pair formation despite attractive interactions.
- The phase transition exhibits Kosterlitz-Thouless quantum-critical behavior.

## Abstract

We show that a random interacting model exhibits solvable non-Fermi liquid behavior and exotic pairing behavior. This model, dubbed as the Yukawa-SYK model, describes the random Yukawa coupling between $M$ quantum dots each hosting $N$ flavors of fermions and $N^2$ bosons that self-tunes to criticality at low energies. The diagrammatic expansion is controlled by $1/MN$, and the results become exact in a large-$M$, large-$N$ limit. We find that pairing only develops within a region of the $(M,N)$ plane --- even though the pairing interaction is strongly attractive, the incoherence of the fermions can spoil the forming of Cooper pairs, rendering the system a non-Fermi liquid down to zero temperature. By solving the Eliashberg equation and the renormalization group equation, we show that the transition into the pairing phase exhibits Kosterlitz-Thouless quantum-critical behavior.