Exactly solvable pairing models in two dimensions

TL;DR

This paper introduces a family of exactly solvable two-dimensional pairing models with arbitrary momentum pairs, revealing potential ground states related to high-temperature superconductivity and identifying a quantum phase transition.

Contribution

It presents a new class of exactly solvable pairing Hamiltonians in two dimensions, extending beyond traditional zero-momentum pair models.

Findings

All models in the family are exactly solvable.

The models include ground states relevant to high-temperature superconductivity.

An analytical expression for energy and a quantum phase transition are identified.

Abstract

The BCS theory models electron correlations with pure zero-momentum pairs. Here we consider a family of pairing Hamiltonians, where the electron correlations are modelled with pure arbitrary-momentum pairs. We find all models in the family are exactly solvable, and present these solutions. It is interesting to note that the $\eta$ pair or the $d$ -wave pair condensate in $T_{c}$ superconductivity can be the ground state of a Hamiltonian in the family. These models are two-dimensional because only the z-component of the total electron spin $S_z$ is conserved. Significantly, for the $\eta$ pair or $d$ -wave pairing model in the family we find an analytical expression of energy and an abrupt ground state change from independent particle state to the $d$ -wave pair condensate, suggesting a quantum phase transition.