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arXiv:cond-mat/9609231 · Physical review. B, Condensed matter

Dynamical density-density correlations in one-dimensional Mott insulators

W. Stephan, Karlo Penc

Published Dec 15, 1996• 56 citations
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Abstract

The dynamical density-density correlation function is calculated for the one-dimensional, half-filled Hubbard model extended with nearest-neighbor repulsion using the L\'anczos algorithm for finite-size systems and analytically for large on-site repulsion compared to hopping amplitudes. At the zone boundary an excitonic feature exists for any finite nearest-neighbor repulsion and exhausts most of the spectral weight, even for parameters where no exciton is visible at zero momentum.

DOI
10.1103/physrevb.54.r17269

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The dynamical density-density correlation function is calculated for the one-dimensional, half-filled Hubbard model extended with nearest-neighbor repulsion using the L'anczos algorithm for finite-size systems and analytically for large on-site repulsion compared to hopping amplitudes. At the zone boundary an excitonic feature exists for any finite nearest-neighbor repulsion and exhausts most of the spectral weight, even for parameters where no exciton is visible at zero momentum.
We employ dynamical density-matrix renormalization-group (DDMRG) and field-theory methods to determine the frequency-dependent optical conductivity in one-dimensional extended, half-filled Hubbard models. The field-theory approach is applicable to the regime of ``small'' Mott gaps which is the most difficult to access by DDMRG. For very large Mott gaps the DDMRG recovers analytical results obtained previously by means of strong-coupling techniques. We focus on exciton formation at energies below the onset of the absorption continuum. As a consequence of spin-charge separation, these Mott-Hubbard excitons are bound states of spinless, charged excitations (``holon-antiholon'' pairs). We also determine exciton binding energies and sizes. In contrast to simple band insulators, we observe that excitons exist in the Mott-insulating phase only for a sufficiently strong intersite Coulomb repulsion. Furthermore, our results show that the exciton binding energy and size are not related in a simple way to the strength of the Coulomb interaction.
We employ dynamical density-matrix renormalization-group (DDMRG) and field-theory methods to determine the frequency-dependent optical conductivity in one-dimensional extended. half-filled Hubbard models. The field-theory approach is applicable to the regime of "small" Mott gaps which is the most difficult to access by DDMRG. For very large Mott gaps the DDMRG recovers analytical results obtained previously by means of strong-coupling techniques. We focus on exciton formation at energies below the onset of the absorption continuum. As a consequence of spin-charge separation, these Mott-Hubbard excitons are bound states of spinless, charged excitations ("holon-antiholon" pairs). We also determine exciton binding energies and sizes. In contrast to simple band insulators, we observe that excitons exist in the Mott-insulating phase only for a sufficiently strong intersite Coulomb repulsion. Furthermore, our results show that the exciton binding energy and size are not related in a simple way to the strength of the Coulomb interaction.
We study a generalized Hubbard model with on-site interaction U, nearest-neighbor repulsion V, and general correlated hopping under the condition that the number of doubly occupied sites is conserved. We find the exact ground state (GS) in arbitrary dimension in two wide regions of parameters. In one of them the GS is a Mott insulator (MI) and in the other it is a charge-density wave (CDW). The boundary of the MI and a large part of that of the CDW are determined exactly for relevant lattices. We study numerically the effect of relaxing the above-mentioned condition.
The density-matrix renormalization group is used to study the phase diagram of the one-dimensional half-filled Hubbard model with on-site (U) and nearest-neighbor (V) repulsion and hopping t. A critical line V(c)(U) approximately U/2 separates a Mott insulating phase from a charge-density-wave phase. The formation of bound charge excitations for V>2t changes the phase transition from continuous to first-order at a tricritical point U(t) approximately 3.7t, V(t)=2t. A frustrating effective antiferromagnetic spin coupling induces a bond-order-wave phase on the critical line V(c)(U) for U(t)<U less, similar 7t.
An extended Hubbard model that includes not only on-site but also intersite Coulomb repulsion and distant transfer is numerically investigated using the exact Lanczos diagonalization method for finite-size systems up to L=20L=20L=20 sites. The aim is to study the charge order and unconditional dimerization of a chain at density $\ensuremath{\rho}=0.4$. From the analysis of the spin and charge correlation functions, we deduce the formation of a dimer insulating state which is a Wigner lattice-type charge ordered state. The next-nearest-neighbor hopping t2{t}_{2}t2​ enhances the intradimer correlations and weakens the interdimer correlations. Implications for the CuO2\mathrm{Cu}{\mathrm{O}}_{2}CuO2​ chains in Sr14Cu24O41{\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}Sr14​Cu24​O41​ are discussed.