Bond-order waves

Last, it is well known that the ground state of the EPH model shows a Bond Order Wave if U > 2V and a Charge Density Wave in the other case [43]. In figure (10), we show the relative error of the RVA results compared to the DMRG ones for several choices of Coulombic parameters in function of the dimerization parameter A, in the two different regimes. Once again, the results show clearly that our ansatz is better when A increases. Moreover, its behaviour seems different in the two sides of the... 

At some critical temperature, a structural distortion to dimerized chains occurs together with the opening of a gap in the magnetic excitations. Such a distortion is attributable to a 2kF spin-Peierls transition, just as in MEM(TCNQ)2 (cf. Section III.A.7). A 2kF transition results into chain tetramerization for p = 5 and into chain dimerization for p = 1, as also shown in Fig. 5. For instance, the spin-Peierls transition takes place at T sp = 395 K in KTCNQ and at TsP = 381 K in RbTCNQ [67] (a second form, called RbTCNQ II, also exists for the Rb salt [69], but it is not considered here). By analogy with the case of polymers, the dimerized phase at low temperature is also called a bond-ordered-wave (BOW) phase [47]. 

In the ground-state, the molecular structure can be schematically drawn as having alternating single and double bonds (a bond order wave with periodicity 2a) which are respectively longer and shorter than the equilibrium value of the bond length in (CH). The corresponding electronic structure is that of a 1-d... 

In the presence of Umklapp scattering, the following susceptibilities will be considered for the Peierls channel at 2k% one has the on-site p, = SDW for spin-density-wave and p = BOW for the bond-order-wave in the Cooper channel, one has singlet p = SS and triplet p=TS superconducting correlations. At two-loop level, the auxiliary responses are governed by the flow equations... 

However, when U = 2V, which is the CDW/BOW (Bond Order Wave) transition point, we find that the Hubbard chains have higher third-order polarizability than their counterparts in the f/ — F model. This trend is observed only for 7 and is not seen for the polarizability a. 

As shown in Fig. 3, the calculation for the large-U case allo ws a satisfactory fit of both the conductivity and the reflectance spectra. Note that the plasma edge in reflectance, the conductivity levels in the infrared, and the e-mv structure are simultaneously fitted to a reasonable level of accuracy, although further refinement of the parameter values is still possible. The parameters used are collected in Table 1. The corresponding picture of the electronic structure exhibits a total bandwidth of 1 eV, with a small gap of amplitude 2 A, = 66 meV, associated with a bond-order wave. The gap opens at the Fermi surface, which is shifted... 

An electronic state has a broken symmetry if its symmetry is lower than the Hamiltonian that describes it. Broken symmetry ground states occur widely in Nature, for example, in superconductivity, magnetism, and in particle physics (Anderson 1984). Generally, electron systems in one-dimension can exhibit three types of broken symmetries spin-density waves, charge-density waves, and bond order waves. These waves exhibit particular tjrpes of long range correlation, respectively in the spin-density, charge-density, or bond order. 

In an undimerized chain a spin-density wave exhibits gapless spin excitations and gapped charged excitations. However, in a dimerized chain all three types of order exhibit gapped spin and charge excitations. In fact, for a dimerized chain the spin-density and bond order waves coexist. Mazumdar and Campbell have shown (Mazumdar and Campbell 1985) that the Pariser-Pople-Parr model will exhibit a broken-symmetry ground state provided that. 

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