108 research outputs found
Kubo formula for finite size systems
We demonstrate that the proper calculation of the linear response for
finite-size systems can only be performed if the coupling to the leads/baths is
explicitly taken into consideration. We exemplify this by obtaining a Kubo-type
formula for heat transport in a finite-size system coupled to two thermal
baths, kept at different temperatures. We show that the proper calculation
results in a well-behaved response, without the singular contributions from
degenerate states encountered when Kubo formulae for infinite-size systems are
inappropriately used for finite-size systems.Comment: 4 pages, 1 figur
Holstein polaron: the effect of multiple phonon modes
We generalize the Momentum Average approximations MA and MA
to study the effects of coupling to multiple optical phonons on the properties
of a Holstein polaron. As for a single phonon mode, these approximations are
numerically very efficient. They become exact for very weak or very strong
couplings, and are highly accurate in the intermediate regimes, {\em e.g.} the
spectral weights obey exactly the first six, respectively eight, sum rules. Our
results show that the effect on ground-state properties is cumulative in
nature. In particular, if the effective coupling to one mode is much larger
than to the others, this mode effectively determines the GS properties.
However, even very weak coupling to a second phonon mode has important
non-perturbational effects on the higher energy spectrum, in particular on the
dispersion and the phonon statistics of the polaron band
Holstein magneto-polarons: from Landau levels to Hofstadter butterflies
We study the Holstein polaron in transverse magnetic field using
non-perturbational methods. At strong fields and large coupling, we show that
the polaron has a Hofstadter spectrum, however very distorted and of lower
symmetry than that of a (heavier) bare particle. For weak magnetic fields, we
identify non-perturbational behaviour of the Landau levels not previously
known.Comment: 4 pages, 4 figure
Green's function of a dressed particle
We present a new, highly efficient yet accurate approximation for the Green's
functions of dressed particles, using the Holstein polaron as an example.
Instead of summing a subclass of diagrams (e.g. the non-crossed ones, in the
self-consistent Born approximation (SCBA)), we sum all the diagrams, but with
each diagram averaged over its free propagators' momenta. The resulting Green's
function satisfies exactly the first six spectral weight sum rules. All higher
sum rules are satisfied with great accuracy, becoming asymptotically exact for
coupling both much larger and much smaller than the free particle bandwidth.
Possible generalizations to other models are also discussed.Comment: 4 pages, 3 figure
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