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arXiv:cond-mat/9607194

The Density Matrix Renormalization Group Studies of Metal-Halogen Chains within a Two-Band Extended Peierls-Hubbard Model

Y. Anusooya, Swapan Kumar Pati, S. Ramasesha

Published Jul 26, 1996• 0 citations
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Abstract

The phase diagram of halogen-bridged mixed-valent metal complexes ($MX$) has been studied using a two-band extended Peierls-Hubbard model employing the recently developed Density Matrix Renormalization Group method. We present the energies, charge and spin density distributions, bond orders, charge-charge and spin-spin correlations, in the ground state for different parameters of the model. The effect of bond alternation and site-diagonal distortion on the ground state properties are considered in detail. We observe that the site-diagonal distortion plays a significant role in deciding the nature of the ground state of the system. We find that while the $CDW$ and $BOW$ phases can coexist, the $CDW$ and $SDW$ phases are exclusive in most of the cases. We have also studied the doped $MX$ chains both with and without bond alternation and site-diagonal distortion in the $CDW$ as well as $SDW$ regimes. We find that the additional charge in the polarons and bipolarons for hole doping are confined to a few sites, in the presence of bond alternation and site-diagonal distortion. For electron doping, we find that the additional charge(s) is(are) smeared over the entire chain length and although energetics imply a disproportionation of the negatively charged bipolaron, the charge and spin density distributions do not reflect it. Positively charged bipolaron disproportionates into two polarons in the $SDW$ region. There is also bond order evidence for compression of bond length for the positively charged polaronic and bipolaronic systems and an elongation of the bonds for systems with negatively charged polarons and bipolarons.

DOI
10.48550/arxiv.cond-mat/9607194

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The phase diagram of halogen-bridged mixed-valent metal complexes (MXMXMX) has been studied using a two-band extended Peierls-Hubbard model employing the recently developed Density Matrix Renormalization Group method. We present the energies, charge and spin density distributions, bond orders, charge-charge and spin-spin correlations, in the ground state for different parameters of the model. The effect of bond alternation and site-diagonal distortion on the ground state properties are considered in detail. We observe that the site-diagonal distortion plays a significant role in deciding the nature of the ground state of the system. We find that while the CDWCDWCDW and BOWBOWBOW phases can coexist, the CDWCDWCDW and SDWSDWSDW phases are exclusive in most of the cases. We have also studied the doped MXMXMX chains both with and without bond alternation and site-diagonal distortion in the CDWCDWCDW as well as SDWSDWSDW regimes. We find that the additional charge in the polarons and bipolarons for hole doping are confined to a few sites, in the presence of bond alternation and site-diagonal distortion. For electron doping, we find that the additional charge(s) is(are) smeared over the entire chain length and although energetics imply a disproportionation of the negatively charged bipolaron, the charge and spin density distributions do not reflect it. Positively charged bipolaron disproportionates into two polarons in the SDWSDWSDW region. There is also bond order evidence for compression of bond length for the positively charged polaronic and bipolaronic systems and an elongation of the bonds for systems with negatively charged polarons and bipolarons.
The phase diagram of halogen-bridged mixed-valence metal complexes (MX) has been studied using a two-band extended Peierls-Hubbard model employing the recently developed density-matrix renormalization group method. We present the energies, charge- and spin-density distributions, bond orders, and charge-charge and spin-spin correlations, for the ground state, for different parameters of the model. The effects of bond alternation and site-diagonal distortion on the ground-state properties are considered in detail. We observe that the site-diagonal distortion plays a significant role in deciding the nature of the ground state of the system. We find that while the charge-density-wave (CDW) and bond-order-wave (BOW) phases can coexist, the CDW and SDW (spin-density-wave) phases are mutually exclusive in most cases. We have also studied the doped MX chains both with and without bond alternation and site-diagonal distortion in the CDW as well as SDW regimes. We find that the additional charges in the polarons and bipolarons for hole doping are confined to a few sites, in the presence of bond alternation and site-diagonal distortion. For electron doping, we find that the additional charge(s) is (are) smeared over the entire chain length, and although the energetics implies a disproportionation of the negatively charged bipolaron, the charge- and spin-density distributions do not reflect this. A positively charged bipolaron disproportionates into two polarons in the SDW region. There is also bond-order evidence for compression of the bond length for the positively charged polaronic and bipolaronic systems and an elongation of the bonds for systems with negatively charged polarons and bipolarons.
We revisit the ground-state phase diagram of the one-dimensional half-filled extended Hubbard model with on-site (U) and nearest-neighbor (V) repulsive interactions. In the first half of the paper, using the weak-coupling renormalization-group approach (g(g(g-ology) including second-order corrections to the coupling constants, we show that bond-charge-density-wave (BCDW) phase exists for $U\ensuremath{\approx}2V$ in between charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons disfavors the BCDW state and leads to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line. In the second half of the paper, we investigate the phase diagram of the extended Hubbard model with either additional staggered site potential $\ensuremath{\Delta}$ or bond alternation $\ensuremath{\delta}.$ Although the alternating site potential $\ensuremath{\Delta}$ strongly favors the CDW state (that is, a band insulator), the BCDW state is not destroyed completely and occupies a finite region in the phase diagram. Our result is a natural generalization of the work by Fabrizio, Gogolin, and Nersesyan [Phys. Rev. Lett. 83,83,83, 2014 (1999)], who predicted the existence of a spontaneously dimerized insulating state between a band insulator and a Mott insulator in the phase diagram of the ionic Hubbard model. The bond alternation $\ensuremath{\delta}$ destroys the SDW state and changes it into the BCDW state (or Peierls insulating state). As a result the phase diagram of the model with $\ensuremath{\delta}$ contains only a single critical line separating the Peierls insulator phase and the CDW phase. The addition of $\ensuremath{\Delta}$ or $\ensuremath{\delta}$ changes the universality class of the CDW-BCDW transition from the Gaussian transition into the Ising transition.
Phase diagrams of the one-dimensional extended Hubbard model with a nearest neighbor interaction VVV and site-off-diagonal (bond-charge XXX and bond-bond WWW) interactions at half-filling are obtained numerically, using the level-crossing approach for finite-size clusters. This analysis is straightforward extension of the preceding work [cond-mat/9909277], where only the XXX term is considered as a site-off-diagonal term. Similarly to the XXX term, the WWW term enlarges bond-charge-density-wave (BCDW) and bond-spin-density-wave (BSDW) phases for W<0W<0W<0 and W>0W>0W>0 cases, respectively. In the strong-coupling region, however, the WWW term causes ferromagnetism for W>0W>0W>0, and shifts the boundary of the phase separation in the U/t≪−1U/t\ll-1U/t≪−1 region, which are different from the roles of the XXX term. In addition, we discuss a parameter region where the BSDW state is the exact ground state, and show that the exactly solvable point appears just on the phase boundary between the BSDW and the ferromagnetic phases.
Discrepancies between the single-particle band structure and the exact many-particle behavior are particularly striking in one-dimensional systems. The one-dimensional alternating Hubbard model is especially interesting as a nontrivial model for conjugated polymer chains, such as polyacetelyne. We study this model for chains of 60 sites using the density-matrix renormalization-group method. We obtain the first electronic and magnetic excited-state energies at half filling as a function of an alternating hopping parameter and on-site electron-electron interaction. We also study the effect of the interaction on the dimerization and discuss its relation to the charge gap and spin triplet gap. In addition, we calculate the local spin and charge densities of some excited states, which manifest a clear crossover from bandlike to strongly correlated behavior.
Exact-diagonalization and quantum Monte Carlo methods are used to study the occurrence of a metal-insulator transition and the distribution of charges and magnetic moments in the ground state of a one- and two-dimensional half-filled system of correlated electrons, described by a one-band simplified Hubbard model extended with bond-charge--site-charge interactions. Numerical results for the electrical conductivity, the density of states, and the spin- and charge-density correlation functions strongly suggest that the bond-charge--site-charge interaction plays a fundamental role in the occurrence of a metal-insulator transition and of ferromagnetic order.
To the conventional Peierls-Hubbard model, involving both on-site (U) and nearest-neighbor (V) Coulomb repulsions, we add ``off-diagonal'' terms, not expressible purely in terms of site densities, representing bond-bond (W) and mixed bond-site (X) electron-electron repulsive interactions involving nearest neighbors. We review earlier analyses of these interactions and discuss relative magnitudes of the parameters in applications to real materials. As a specific illustration, we investigate the effects of the off-diagonal W and X terms on dimerization in the one-dimensional, half-filled-band Peierls-Hubbard models, which have been widely applied to conjugated polymers (such as trans-polyacetylene) and to related quasi-one-dimensional charge-density wave (CDW) systems. Using both weak- and strong-coupling perturbation theory for large systems and exact diagonalizations of small systems, we investigate thoroughly the nature of the ground state of the model. For a broad range of the site-diagonal Hubbard parameters (U,V), including the values believed to be relevant to trans-polyacetylene, we find that the off-diagonal terms (W,X) initially enhance dimerization, thereby stabilizing the dimerized [or bond-order-wave (BOW)] ground state. For (unphysically) large values of W relative to U and V, dimerization is destroyed, and the BOW ground state goes over to a ferromagnetic ground state or a CDW ground state, depending on the relative sizes of U, V, and W. We conclude with a general discussion of the applicability of the Peierls-Hubbard models to quasi-one-dimensional materials, including the potential importance of the breaking of charge conjugation (``particle-hole'') symmetry by the X term.