Jmp. Carmelo et Nmr. Peres, COMPLETE PSEUDOHOLE AND HEAVY-PSEUDOPARTICLE OPERATOR REPRESENTATION FOR THE HUBBARD CHAIN, Physical review. B, Condensed matter, 56(7), 1997, pp. 3717-3741
We introduce the pseudohole and heavy-pseudoparticle operator algebra
that generates all Hubbard-chain eigenstates from a single reference v
acuum. In addition to the pseudoholes already introduced for the descr
iption of the low-energy physics, this involves the heavy pseudopartic
les associated with Hamiltonian eigenstates whose energy spectrum has
a gap relative to-the many-electron ground state. We introduce a gener
alized pseudoparticle perturbation theory that describes the relevant
finite-energy ground-state transitions. In the present basis these exc
itations refer to a small density of excited pseudoparticles. Our oper
ator basis goes beyond the Bethe-ansatz solution and it is the suitabl
e and correct starting point for the study of the finite-frequency pro
perties, which are of great relevance for the understanding of the unu
sual spectral properties detected in low-dimensional novel materials.