The Holstein polaron: results from numerical and analytical ... - PiTP
The Holstein polaron: results from numerical and analytical ... - PiTP
The Holstein polaron: results from numerical and analytical ... - PiTP
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Most <strong>numerical</strong> approaches focus on the evolution of the <strong>polaron</strong> b<strong>and</strong> (low-energy properties)<br />
variational methods (Trugman <strong>and</strong> co-workers)<br />
truncate size of cloud (both spatial <strong>and</strong> how many phonons are allowed) Lanczos<br />
advantages: continuous k (not a finite-size chain!); matrix elements are very simple to get, can be<br />
extremely accurate for discrete states (like the <strong>polaron</strong> b<strong>and</strong> of interest)<br />
disadvantages: at large couplings, very many phonon combinations huge dimension of<br />
variational Hilbert space (gets worse in higher dimension). Also, no predictive powers for the<br />
continuum above the <strong>polaron</strong> b<strong>and</strong> nothing about high-energy properties.
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