Spectral signatures of the Luttinger liquid to the charge-density-wave transition

Abstract

Electron-and phonon spectral functions of the one-dimensional, spinless-fermion Holstein model at half filling are calculated in the four distinct regimes of the phase diagram, corresponding to an attractive or repulsive Luttinger liquid at weak electron-phonon coupling, and a band-or polaronic insulator at strong coupling. The results obtained by means of kernel polynomial and systematic cluster approaches reveal substantially different physics in these regimes and further indicate that the size of the phonon frequency significantly affects the nature of the quantum Peierls phase transition, the latter being either of the soft-mode or central-peak type. The generic features observed are relevant to several classes of low-dimensional materials.

Phase diagram of the one-dimensional Hubbard-Holstein model at half and quarter filling

“…15 find the intermediate phase existing in a narrow region on both sides of the U eff = 0 line, while we find the intermediate phase only for U eff Ͻ 0. Several calculations of the single-particle spectral function are available for the HHM, [41][42][43] the spinless Holstein model, 44,45 as well as the d = ϱ studies previously mentioned. In Ref.…”

Lang-Firsov Approaches to Polaron Physics: From Variational Methods to Unbiased Quantum Monte Carlo Simulations

“…These peaks-not present at T = 0 [50,51]-arise from thermally activated transitions to states with additional phonons excited, and are also visible in figures 11 and 13. While for WC (λ = 0.1, figure 11), the maximum of these features is almost exactly located at |ω − µ| = ω 0 , it moves to |ω − µ| ≈ 1.25ω 0 for IC (λ = 1, figure 15), and finally to |ω − µ| ≈ 2.5ω 0 for SC (λ = 2, figure 13).…”

“…Clearly, for small n, there is a peak with large spectral weight at the Fermi level. In contrast, for large n, the tendency toward formation of a Peierls-(band-) insulating state at n = 0.5 suppresses the DOS at the Fermi level, although we are well below the critical value of λ at which the cross-over to the insulating state takes place at T = 0 [49,50]. The additional small features separated from µ by the bare phonon energy ω 0 will be discussed below.…”

“…Now, the photoemission spectrum for k < π/2 is almost symmetric to the inverse photoemission spectrum for k > π/2 and already reveals the gapped structure which occurs at n = 0.5 due to charge-density-wave formation accompanied by a Peierls distortion [50].…”

“…with the one-electron states (50). Introducing the matrix elements (Ω) ij = i| Ω |j and the expectation value with respect to w b ,…”