On the Validity of the Tomonaga Luttinger Liquid Relations for the One-dimensional Holstein Model

Abstract

For the one-dimensional Holstein model, we show that the relations among the scaling exponents of various correlation functions of the Tomonaga Luttinger liquid (LL), while valid in the thermodynamic limit, are significantly modified by finite size corrections. We obtain analytical expressions for these corrections and find that they decrease very slowly with increasing system size. The interpretation of numerical data on finite size lattices in terms of LL theory must therefore take these corrections into account. As an important example, we re-examine the proposed metallic phase of the zero-temperature, half-filled one-dimensional Holstein model without employing the LL relations. In particular, using quantum Monte Carlo calculations, we study the competition between the singlet pairing and charge ordering. Our results do not support the existence of a dominant singlet pairing state.

7 pages

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Cited by in corpus (9)

• Excitation spectra and spin gap of the half-filled Holstein-Hubbard model
• Effect of Electron-Phonon Interaction Range for a Half-Filled Band in One Dimension
• Nature of ground states in one-dimensional electron-phonon Hubbard models at half-filling
• Finite-size effects in Luther-Emery phases of Holstein and Hubbard models
• Density waves in strongly correlated quantum chains
• Dominant Superconducting Fluctuations in the One-Dimensional Extended Holstein-Extended Hubbard model
• Phonon Induced Instabilities in Correlated Electron Hamiltonians
• Peierls to superfluid crossover in the one-dimensional, quarter-filled Holstein model
• The one-dimensional Holstein model revisited