Broken Symmetries in the One-Dimensional Extended Hubbard Model

The past two decades have witnessed the discoveries of several new classes of novel electronic materials. Ranging from conducting polymers through charge transfer solids and inorganic chain compounds to organic and high temperature superconductors, these materials have in common two important, unusual properties. First, their electronic structures are strongly anisotropic, in some cases (e.g., the chain-like conducting polymers) rendering them quasi-one dimensional, and in others (e.g., the planar copper oxide-based high temperature (“high Tc” ) superconductors) causing them to be quasi-two dimensional. Second, electron-electron Coulomb interactions play a considerably more important role than in normal metals [1]. Accordingly, considerable recent theoretical effort has been directed towards (idealized) models of “strongly correlated electrons in reduced dimensions,” the most celebrated example of which is the one-dimensional Hubbard model. In the Hubbard Hamiltonian, the Coulomb interactions are caricatured by a single parameter U representing the repulsion when two electrons occupy the same site. Remarkably, this model is “integrable” [2] in that an exact solution can be obtained by Bethe Ansatz techniques [3]. Despite its considerable analytic appeal and historical importance, the one-dimensional Hubbard model is limited in its applicability to the real novel materials, in which there is considerable evidence for the essential role of longer-ranged Coulomb interactions. For instance, the “excitonic” effects observed in conducting polymers such as polydiacetylene (PDA) and poly-paraphenylene-vinylene (PPV) can not be explained [1; 4] without invoking at least a nearest-neighbor Coulomb repulsion, conventionally called V . Considering simultaneously both an on-site U and a nearest-neighbor V leads to the “extended Hubbard model”, which has recently been the subject of intense interest. In its onedimensional variant, appropriate for modeling conducting polymers, certain charge-transfer solids, and related materials, the extended Hubbard model is described by the Hamiltonian