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

More documents

Recommendations

Info

Why should this be a reasonable thing to do? (i) Real-space argument: MA (0) means i j i j At low energies ω ~ E GS < -2dt free electron Greens’ functions decrease exponentially with distance |i-j| MA (0) keeps the most important (diagonal) contribution. <strong>The</strong> approximation becomes better the more phonons are present, since the lower ω – n Ω is, the faster the decay. Expect ground-state properties to be described quite accurately.
(ii) Spectral weight sum rules (see PRB 74, 245104 (2006) for details) can be calculated exactly MA (0) satisfies exactly the first 6 sum rules, <strong>and</strong> with good accuracy all the higher ones. Note: it is not enough to only satisfy a few sum rules, even if exactly. ALL must be satisfied as well as possible. Examples: 1. SCBA satisfies exactly the first 4 sum rules, but is very wrong for higher order sum rules fails miserably to predict strong coupling behavior (proof coming up in a minute). 2. Compare these two spectral weights: -w 0 0 w 0
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 and 8: infinitely strong coupling, t=0 ele
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 32: Since G(k,w) is a sum of diagrams,

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

Create successful ePaper yourself

Delete template?

Save as template?