The Holstein polaron: results from numerical and analytical ... - PiTP

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weak coupling, g = “small” low-energy eigenstates of known k: with eigenenergies (for k< k cross ) E k The phonons can be quite far spatially from the electron large polaron polaron + one- phonon continuum (finite lifetimes) k Ω polaron band (infinitely long-lived quasiparticle) high-k: wavefunction dominated by el+1ph contributions low-k: wavefunction dominated by free electron contribution
infinitely strong coupling, t=0 electron stays at a single site forever n i =1 there, 0 elsewhere → polaron binding energy; small polaron limit only discrete eigenstates! Recall coherent states:
Page 1 and 2: The Holstein polaron: results from
Page 3 and 4: Model of interest: the Holstein Ham
Page 5: (spin is irrelevant, N = number of
Page 9 and 10: Quantity of interest: the Green’s
Page 11 and 12: Most numerical approaches focus on
Page 13 and 14: Quantum Monte Carlo methods (Kornil
Page 15 and 16: New proposal: the MA (n) hierarchy
Page 19 and 20: 3D Polaron dispersion L. -C. Ku, S.
Page 21 and 22: MA (0) is remarkably good, especial
Page 23 and 24: details in PRB 76, 165109 (2007) (m
Page 25 and 26: 1D, Ω =0.5t, λ =0.25
Page 27: Our answer to how spectral weight e
Page 30 and 31: Why should this be a reasonable thi
Page 32: Since G(k,w) is a sum of diagrams,

The Holstein polaron: results from numerical and analytical ... - PiTP

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