Coherent pairing states for the Hubbard model

TL;DR

This paper introduces coherent pairing states for the Hubbard model on bipartite lattices, enabling exact calculations of physical properties and providing a complementary perspective to BCS superconductivity.

Contribution

It defines a new class of coherent pairing states based on $ ext{eta}$-pairing operators, allowing exact analysis of the Hubbard model's properties.

Findings

Exact calculation of energy and fluctuations

Determination of pairing off-diagonal long-range order (ODLRO)

States are superconducting but not eigenstates of the Hamiltonian

Abstract

We consider the Hubbard model and its extensions on bipartite lattices. We define a dynamical group based on the $\eta$-pairing operators introduced by C.N.Yang, and define coherent pairing states, which are combinations of eigenfunctions of $\eta$-operators. These states permit exact calculations of numerous physical properties of the system, including energy, various fluctuations and correlation functions, including pairing ODLRO to all orders. This approach is complementary to BCS, in that these are superconducting coherent states associated with the exact model, although they are not eigenstates of the Hamiltonian.