Hubbard density wave

Figure 1.19. Generic T-P phase diagram for BFS. The origin on the pressure axis is arbitrarily set for (TMTTF)2PF6. MH, Mott-Hubbard M, Metal SP, Spin-Peierls AF, Antiferromagnetic SDW, Spin-Density-Wave SC, Superconductor. Adapted from Auban-Senzier J6rome, 2003.

At = 0.1 there are both Mott-Hubbard and Mott-Wannier excitons, forming two inter-related families of essential states. In general, the B states are linear superpositions of eqns (6.22) and (6.30), while the states are linear superpositions of eqns (6.23) and (6.31). As the bond dimerization decreases the spin-density-wave component of the state increases (Mukhopadhyay et al. 1995). Figure 6.10(c) shows the l H, 2 A+, and 4 H states, predominately forming the Mott-Wannier family of excitons, while Fig. 6.10(d) shows the l B, ... 

The effects of electron-phonon interactions alone were described in Chapter 4. We showed that these interactions lead to a dimerized, semiconducting ground state and to solitonic structures in the excited states. On the other hand, the effects of electron-electron interactions in a polymer with a fixed geometry were described in Chapters 5 and 6. There it was shown that the electronic interactions cause a metal-insulator (or Mott-Hubbard) transition in undimerized chains. Electron-electron interactions also cause Mott-Wannier excitons in the weak-coupling limit of dimerized chains, and to both Mott-Hubbard excitons and spin density wave excitations in the strong coupling limit. 

A variety of munerical methods have been used to elucidate the existence of phase separation in the groimd states of the Hubbard and models of the Cu-0 planes of cuprate perovskites. States with charge density waves (CDW), which can be interpreted as stripes, were obtained in Refs. [24-26,29-32] by using the mean-field approximation, the variational principle with the Gutzwiller-type variational fimctions, and the density matrix renormalization group calculations. However, the results of the Monte Carlo simulations [33-35] and cluster calculations [36,37] cast doubt on this finding. Thus, the issue of whether a purely electronic mechanism can explain the stripe formation is still an open question. 

In the case of delocalized basis states tpa(r), the main matrix elements are those with 0 = 7 and f3 = 6, because the wave functions of two different states with the same spin are orthogonal in real space and their contribution is small. It is also true for the systems with localized wave functions tpa(r), when the overlap between two different states is weak. In these cases it is enough to replace the interacting part by the Anderson-Hubbard Hamiltonian, describing only density-density interaction... 

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