{'fraction_non_alphanumeric': 0.046052631578947366, 'fraction_numerical': 0.00860323886639676, 'mean_word_length': 4.762390670553936, 'pattern_counts': {'":': 0, '<': 1, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 2, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Many-polaron problem by cluster perturbation theory

The carrier-density dependence of the photoemission spectrum of the Holstein many-polaron model is studied using cluster perturbation theory combined with an improved cluster diagonalization by Chebychev expansion.

Polaronic quasiparticles originating from strong electron-phonon interaction play an important role in polar solids, including alkali halides, transition metal oxides/perovskites and, in particular, quasi onedimensional (1d) materials such as MX chains, conjugated polymers or organic charge-transfer complexes. However, the theoretical description of the underlying models represents a challenging open problem.
Recently, significant effects of finite carrier density on the spectral properties of a polaronic system have been discovered for the spinless Holstein model [1], revealing the shortcomings of widely used single-polaron theories. The Hamiltonian of the 1d tight-binding (t) Holstein model reads Here c † i (b † i ) creates a spinless fermion (a phonon) at lattice site i, andni = c † i c i . The parameters are the adiabaticity ratio ω0/t, and the dimensionless coupling constant λ = Ep/2t, with the polaron binding energy Ep.
[3] and references therein) yields accurate results in the thermodynamic limit.
Here, we calculate the zero-temperature Green function G(k, ω) = c k ; c † k ω using CPT in combination with a Chebychev expansion technique [4]. The latter does not suffer from the shortcomings of other methods, and exploits the analytical separation of the symmetric phonon mode [5] in order to ensure wellconverged results. Calculations have been done on parallel supercomputers, with the largest matrix dimension exceeding 10 10 . Within CPT, the one-particle Green function is obtained from where G (c) and V denote the corresponding real-space cluster Green function and the intercluster hopping matrix, respectively, and subsequent Fourier transformation [3].
A substantial dependence of the system properties on the band filling is expected for intermediate electron-phonon interaction, for which a large (extended) polaron state is known to exist in the singleelectron case. By contrast, for strong coupling, the polaron size collapses to a single site, so that different carriers will not overlap (interact). Hence, we take λ = 1, the critical coupling for the large-to-small polaron cross-over in the adiabatic regime ω0/t < 1. Note that the abovementioned density effects are absent for ω0/t ≫ 1 [1]. Figure 1 shows results for the one-electron spec-  tral functions A ± (k, ω) = −Im G ± (k, ω)/π, where G − (G + ) corresponds to the (inverse) photoemission part of G, for fixed cluster size N = 10.
In the low density case n = 0.1 ( Fig. 1(a)), we can easily identify a (coherent) polaron band crossing the Fermi level EF, the latter being situated at the point where A − and A + intersect. The band flattens at large k, as known from single-polaron studies. Below this band, there exist equally spaced phonon excitations with small spectral weight, which reflect the Poisson distribution of phonons in the one-electron ground state. Finally, above EF, there is a broad incoherent band whose maximum follows closely the dispersion relation of free particles.
As the density n increases (Figs. 1(a) -(c)) , the gap between the polaron band and the incoherent excitations is reduced, and the low-energy phonon peaks begin to broaden, until they have ultimately merged into a broad band for n = 0.4 ( Fig. 1(d)). More importantly, for n ≥ 0.3, a polaron band can no longer be identified as incoherent excitations lie very close to the Fermi level. Finally, at n = 0.4, the spectrum consists of a broad main band of effective width ≈ 6t crossing EF, as in a metallic system, and low-energy excitations are available. This indicates that the polaronic quasiparticles, existing at small n, have dissociated into dressed electrons due to mutual interaction.