Incommmensurability and Unconventional Superconductor to Insulator Transition in the Hubbard Model with Bond-Charge Interaction

Abstract

We determine the quantum phase diagram of the one-dimensional Hubbard model with bond-charge interaction X in addition to the usual Coulomb repulsion U>0 at half-filling. For large enough X<t the model shows three phases. For large U the system is in the spin-density wave phase as in the usual Hubbard model. As U decreases, there is first a spin transition to a spontaneously dimerized bond-ordered wave phase and then a charge transition to a novel phase in which the dominant correlations at large distances correspond to an incommensurate singlet superconductor.

HiddenXYstructure of the bond-charge Hubbard model

“…Such transition was discovered numerically in Ref. [5] and separates a incommensurate singlet superconducting (ICSS) phase from a bond ordered wave (BOW) phase [6]. As seen in Fig.1, the curve obtained with our mapping describes rather accurately the numerical data of the transition.…”

“…This extension is considered to be especially relevant to the field of high-T c superconductors [4]. In fact, it has recently been found [5,6] that a superconducting phase takes place also for repulsive values of the on-site Coulomb interaction. The phase is characterized by incommensurate modulations in the charge structure factor.…”

Nonlocal Order Parameters for the 1D Hubbard Model

“…The present analysis could be further exploited to extended Hubbard models [14,15], to describe other topologically ordered phases; noticeably, the fully gapped phase characterized by non vanishing charge and spin gaps should correspond to the non vanishing of both O (ν) P 's. Work is in progress along these lines.…”

Topological quantum phase transition between Fermi liquid phases in an Anderson impurity model

“…Some QPTs are topological QPTs (TQPTs): even if some other properties vary continuously at the transition, a topological integer (related with a geometrical Berry phase or the topology of each thermodynamic phase) jumps at the TQPT. Examples of this kind of transitions are several charge and spin TQPTs observed in onedimensional models in which the nearest-neighbor hopping depends on the occupation [11,12] as in cold-atom lattices [13], or the Hubbard model with alternative onsite energies [14,15], for which the topological transition might be observable in transport through arrays of quantum dots or molecules [16].…”