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Solid State Communications

A Peierls-Hubbard model: Exact quantum mechanical results and a variational method

Sigrid M. Weber, H. Büttner

Published Oct 1, 1985• 23 citations
Publisher
DOI
10.1016/0038-1098(85)90410-7

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Physical review. B, Condensed matter•Oct 15, 1993•2 citations
We calculate the superfluid weight and the polarization amplitude for the one-dimensional bosonic Hubbard model with focus on the strong-coupling regime via variational, exact diagonalization, and strong coupling calculations. Our variational approach is based on the Baeriswyl wave function, implemented via Monte Carlo sampling. We derive the superfluid weight appropriately in a variational setting. We emphasize the importance of implementing the Peierls phase in position space and to allow for many-body interference effects, rather than implementing the Peierls phase as single particle momentum shifts. At integer filling, the Baeriswyl wave function gives zero superfluid response at any coupling. At half filling our variational superfluid weight is in reasonable agreement with exact diagonalization results. We also calculate the polarization amplitude, the variance of the total position, and the associated size scaling exponent, which corroborate that this variational approach produces an insulating state at integer filling. Our Baeriswyl based variational method is applicable to significantly larger system sizes than exact diagonalization or quantum Monte Carlo.
A density-matrix renormalization-group (DMRG) method for calculating dynamical properties and excited states in low-dimensional lattice quantum many-body systems is presented. The method is based on an exact variational principle for dynamical correlation functions and the excited states contributing to them. This dynamical DMRG is an alternate formulation of the correction vector DMRG but is both simpler and more accurate. The finite-size scaling of spectral functions is discussed and a method for analyzing the scaling of dense spectra is described. The key idea of the method is a size-dependent broadening of the spectrum. The dynamical DMRG and the finite-size scaling analysis are demonstrated on the optical conductivity of the one-dimensional Peierls-Hubbard model. Comparisons with analytical results show that the spectral functions of infinite systems can be reproduced almost exactly with these techniques. The optical conductivity of the Mott-Peierls insulator is investigated and it is shown that its spectrum is qualitatively different from the simple spectra observed in Peierls (band) insulators and one-dimensional Mott-Hubbard insulators.
The exact solution of the Hubbard-Peierls model is given in a cluster of six atoms and three spinless electrons. Phonons with wave vector k=\ensuremath{\pi} are retained and quantum mechanically analyzed. Energy level and several averages are evaluated, thus determining the physical properties of the model in terms of the parameters of the system. The regime of the distorted lattice is obtained. The exact and Born-Oppenheimer (BO) results are compared, concluding that the BO enhances quantum fluctuations; this peculiar behavior is explained.