Geometrical frustration of an extended Hubbard diamond chain in the quasiatomic limit

Abstract

We study the geometrical frustration of an extended Hubbard model on a diamond chain, where vertical lines correspond to the hopping and repulsive Coulomb interaction terms between sites while the remaining lines represent only the Coulomb repulsion term. The phase diagrams at zero temperature show quite curious phases: five types of frustrated states and four types of nonfrustrated states, ordered antiferromagnetically. Although a decoration transformation was derived for spin-coupling systems, this approach can be applied to electron-coupling systems. Thus the extended Hubbard model can be mapped onto another effective extended Hubbard model in the atomic limit with additional three- and four-body couplings. This effective model is solved exactly using the transfer-matrix method. In addition, using the exact solution of this model, we discuss several thermodynamic properties away from the half-filled band, such as chemical potential behavior, electronic density, and entropy, for which we study geometrical frustration. Consequently, we investigate the specific heat as well.

Flat band states: Disorder and nonlinearity

“…Destructive interference between these two paths can be introduced in a variety of ways, for example by applying a magnetic field 24 or Rashba spin-orbit coupling, 25 which results in wave localization. Interesting interacting phases have also been obtained in the corresponding Hubbard 23,[26][27][28] and Ising models. 29 Here we consider a tight-binding model with mean-field interaction terms, which hosts intersecting dispersive and flat bands at the Brillouin zone edge [ Fig.…”

“…39 While we have considered in this paper a relatively simple tight-binding model, we have verified in a number of other quasi-1D cases 37 that our results should be generic to any system with intersecting flat and dispersive bands. Similarly, the emergence of different dynamical regimes due to the competition between disorder and nonlinearity should be a generic feature of other types of interaction terms, so it would be interesting to extend recent results on interacting bosons and fermions in the ideal diamond chain 23,24,27,28 to disordered systems. There are a variety of settings in which this type of tightbinding model may be realized.…”

Preformed pairs in flat Bloch bands

“…Curiously, much of the work that followed the seminal work by Douçot and Vidal [26] has focused on bosons, more specifically on Josephson junction arrays [21,22,[58][59][60][61][62], also in view of possible applications to topological quantum computing [63]. There are some theoretical works on the diamond chain with fermions [64][65][66][67][68][69][70], however the question of the existence of the local conserved quantities has not been explicitly addressed in any of these works. The only instance where local Z 2 symmetries have been discussed in the case of fermions is Ref.…”

Magnetic and nonmagnetic phases in dopedAB2 t−JHubbard chains

“…In particular, we mention the occurrence of ferrimagnetic GS, in which case we select studies using Hubbard or t-J models [9][10][11][12][13][14][15], including the Heisenberg strong-coupling limit [16][17][18], on chains with AB 2 or ABC topological structures with S GS = 1/2 per unit cell [9-13, 16, 17], which implies ferromagnetic and antiferromagnetic long-range orders [10]. Further, the inclusion of competing interactions or geometrical and kinetic frustration [19][20][21], enlarge the classes of models, thereby allowing ground-states not obeying Lieb or Lieb and Mattis theorems. These studies have proved effective in describing magnetic and other physical properties of a variety of organic, organometallic, and inorganic quasione-dimensional compounds [19,22].…”