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

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Ground-state energy: -2dt (half-bandwidth, at zero coupling) -g 2 /Ω (infinite coupling) Effective coupling as their ratio λ = g 2 /(2dtΩ) weak coupling λ>1 3 energy scales: t, Ω, g 2 dimensionless parameters λ = g 2 /(2dtΩ), Ω/t (d is lattice dimension) very strong coupling, λ>>1 polaron energy is Again, must have a polaron+one-phonon continuum at E GS + Ω details too nasty Question: how is the spectrum evolving between these two very different limits?
Quantity of interest: the Green’s function or propagator eigenenergies and eigenfunctions (1 electron, total momentum k, α is collection of other needed quantum numbers) A(k,ω) = spectral weight, is measured (inverse) angleresolved photoemission spectroscopy (ARPES) η Area is equal to Z Z = quasiparticle weight measures how similar is the true wavefunction to a non-interacting (free electron, no phonons) wavefunction ω
Page 1 and 2: The Holstein polaron: results from
Page 3 and 4: Model of interest: the Holstein Ham
Page 5 and 6: (spin is irrelevant, N = number of
Page 7: infinitely strong coupling, t=0 ele
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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