From electron to small polaron: An exact cluster solution

Abstract

Citation: ALEXANDROV, A.S., 1994. From electron to small polaron: an exact cluster solution. Physical Review B, 49 (14),

Spectral properties of the 2D Holstein polaron

“…Refs. [10][11][12]). This may be originated by the fact, that in the extreme strong-coupling limit both the adiabatic Holstein [2] and non-adiabatic Lang-Firsov [5] formulae, obtained from expansions in powers of α ≪ 1 [2,35] and 1/λ ≪ 1 [36], respectively, yield the same exponential band renormalization: exp{−g 2 }.…”

“…In the weak-coupling (adiabatic) limit, one expects (from scaling arguments) a quasi-free electron behaviour for D > 1, while in a 1D system the carrier state becomes polaronic at arbitrary small λ ("large" polaron). Previous exact diagonalization (ED) work has concentrated on the 1D case [8][9][10][11][12]21,[13][14][15][16][17], where, however, the calculations were limited to either very small clusters, rather weak EP coupling (λ < 1) or to the adiabatic limit (ω o = 0). On the other hand, the most interesting effects will be expected if the characteristic electronic and phononic energy scales are not well separated (λ ∼ 1; α ∼ 1).…”

Dynamical properties of the two-dimensional Holstein-Hubbard model in the normal state at zero temperature: A fluctuation-based effective cumulant approach

“…In addition to the continuous nature of the transition, a kinklike feature is also present near ϭ1, where the transition is observed. The continuity of the ground-state energy is widely accepted on grounds of directdiagonalization studies on finite systems [5][6][7][8] as well as variational calculations. [9][10][11] The kinklike feature has also been reported in one-dimensional calculations but it was attributed to the finite-size effects.…”

“…In this many-body model, the qualitative aspects of the transition from large to small polarons as the electron-phonon ͑e-ph͒ adiabaticity and the Coulomb interaction strengths are varied, with the full assessment of these interactions, is still an unresolved problem since the celebrated work of Holstein. 1 Recently quantum Monte Carlo ͑QMC͒ calculations, 2-4 semianalytic direct diagonalization [5][6][7][8] using finite lattice and electronic degrees of freedom, and variational ground-state techniques [9][10][11] have revealed evidence of a smooth transition of the ground state from the large extended to the small localized polaronic one as the interaction parameters are varied from the weak-coupling adiabatic to strong-coupling antiadiabatic ranges. The ground-state dynamics of the Holstein-Hubbard model is determined by the three dimensionless scales; viz., the adiabaticity ␥ϭt/ 0 , the e-ph mediated coupling ϭ(g/ 0 ) 2 , and the repulsive Coulomb interaction strength V c e-e / 0 where 0 is the frequency of Einstein phonons, t is the charge transfer amplitude and g is the linear e-ph coupling strength.…”

Dimensionality effects on the Su–Schrieffer–Heeger model

“…As the spatial extension of the lattice deformation can vary, the concepts of large and small polaron have been introduced: the transition between a large and a small polaron state is driven by the strength of the electron-phonon coupling [10][11][12][13] and monitored through the behavior of ground state properties such as the polaron energy band and the effective mass [14][15][16]. This transition [17], leading to a self trapped state [18] at strong couplings, is accompanied by a sizeable enhancement of the effective mass whose value may change considerably according to the degree of adiabaticity and the peculiarities of the lattice structure [19,20]. Theoretical investigations usually start from the Holstein molecular crystal model [21] which assumes a momentum independent coupling of electrons to dispersive optical phonons.…”