Speaker
Description
In a one-dimensional lattice anyons can be defined via generalized commutation
relations containing a statistical parameter, which interpolates between the boson
limit and the pseudo-fermion limit. The corresponding anyon-Hubbard model is
mapped to a Bose-Hubbard model via a fractional Jordan-Wigner transformation,
yielding a complex hopping term with a density-dependent Peierls phase. Here we
work out a corresponding Bogoliubov theory. To this end we start with the underlying
mean-field theory, where we allow for the condensate a finite momentum and
determine it from extremizing the mean-field energy. With this we calculate various
physical properties and discuss their dependence on the statistical parameter and
the lattice size. Among them are both the condensate and the superfluid density as
well as the equation of state and the compressibility. Based on the mean-field theory
we then analyse the resulting dispersion of the Bogoliubov quasi-particles, which
turns out to be in accordance with the Goldstone theorem. In particular, this leads to
two different sound velocities for wave propagations to the left and the right, which
originates from parity breaking.
Short bio (50 words) or link to website
https://www-user.rhrk.uni-kl.de/~apelster
| Career stage | Postdoc |
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