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We investigate the influence of the electron-phonon coupling in theone-dimensional spinless Holstein model at half-filling using both a recentlydeveloped projector-based renormalization method (PRM) and an refined exactdiagonalization technique in combination with the kernel polynomial method. Atfinite phonon frequencies the system shows a metal-insulator transitionaccompanied by the appearance of a Peierls distorted state at a finite criticalelectron-phonon coupling. We analyze the opening of a gap in terms of the(inverse) photoemission spectral functions which are evaluated in bothapproaches. Moreover, the PRM approach reveals the softening of a phonon at theBrillouin-zone boundary which can be understood as precursor effect of the gapformation.Comment: 26 pages including 9 figures, final version, as published in Phys.  Rev.

Single-particle excitations and phonon softening in the one-dimensional spinless Holstein model