# Exactly solvable model of strongly correlated $d$-wave superconductivity

## TL;DR

This paper introduces an exactly solvable model of strongly correlated $d$-wave superconductivity using an infinite-dimensional lattice of plaquettes, revealing key mechanisms behind superconductivity and its doping dependence.

## Contribution

It provides an exact solution of a cluster DMFT model exhibiting $d$-wave superconductivity, elucidating the role of pair hopping and phase diagram features.

## Key findings

- Superconductivity arises from a degenerate point in the plaquette phase diagram.
- Pair hopping between $X/Y$-momenta is crucial for the superconducting phase.
- Optimal doping occurs around 0.15, with a Lifshitz transition in the normal state.

## Abstract

We present an infinite-dimensional lattice of two-by-two plaquettes, the quadruple Bethe lattice, with Hubbard interaction and solve it exactly by means of the cluster dynamical mean-field theory. It exhibits a $d$-wave superconducting phase that is related to a highly degenerate point in the phase diagram of the isolated plaquette at that the groundstates of the particle number sectors $N=2,3,4$ cross. The superconducting gap is formed by the renormalized lower Slater peak of the correlated, hole-doped Mott insulator. We engineer parts of the interaction and find that pair hoppings between $X/Y$-momenta are the main two-particle correlations of the superconducting phase. The suppression of the superconductivity in the overdoped regime is caused by the diminishing of pair hopping correlations and in the underdoped regime by charge blocking. The optimal doping is $\sim 0.15$ at which the underlying normal state shows a Lifshitz transition. The model allows for different intra- and inter-plaquette hoppings that we use to disentangle superconductivity from antiferromagnetism as the latter requires larger inter-plaquette hoppings.