Nature of ground states in one-dimensional electron-phonon Hubbard models at half-filling

Abstract

The renormalization group technique is applied to one-dimensional electron-phonon Hubbard models at half-filling and zero temperature. For the Holstein-Hubbard model, the results of one-loop calculations are congruent with the phase diagram obtained by quantum Monte Carlo simulations in the $(U,g_{\mathrm{ph}})$ plane for the phonon-mediated interaction $g_{\mathrm{ph}}$ and the Coulomb interaction $U$. The incursion of an intermediate phase between a fully gapped charge-density-wave state and a Mott antiferromagnet is supported along with the growth of its size with the molecular phonon frequency ${\omega }_0$. We find additional phases enfolding the base boundary of the intermediate phase. A Luttinger liquid line is found below some critical $U^{\ast }\approx g_{\mathrm{ph}}^{\ast }$, followed at larger $U\sim g_{\mathrm{ph}}$ by a narrow region of bond-order-wave ordering which is either charge or spin gapped depending on $U$. For the Peierls-Hubbard model, the region of the $(U,g_{\mathrm{ph}})$ plane with a fully gapped Peierls-bond-order-wave state shows a growing domination over the Mott gapped antiferromagnet as the Debye frequency ${\omega }_D$ decreases. A power law dependence $g_{\mathrm{ph}}\sim U^{2\eta }$ is found to map out the boundary between the two phases, whose exponent is in good agreement with the existing quantum Monte Carlo simulations performed when a finite nearest-neighbor repulsion term $V$ is added to the Hubbard interaction.

11 pages, 10 figures

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Cited by in corpus (10)

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• A functional renormalization group study of the two dimensional Su-Schrieffer-Heeger-Hubbard model
• Continuous-time quantum Monte Carlo for fermion-boson lattice models: Improved bosonic estimators and application to the Holstein model
• Attractive Su-Schrieffer-Heeger-Hubbard Model on a Square Lattice Away from Half-Filling
• Phonon Induced Instabilities in Correlated Electron Hamiltonians
• Optical phonons for Peierls chains with long-range Coulomb interactions
• The one-dimensional Holstein model revisited
• Phase diagram of the two-dimensional Hubbard-Holstein model: enhancement of $s$-wave pairing between charge and magnetic orders