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Exploring Interacting Topological Insulators with Ultracold Atoms: the Synthetic Creutz-Hubbard Model

Thursday, November 9, 2017 - 11:30
Place: 
Donostia International Physics Center
Who: 
Prof. Matteo Rizzi, Johannes-Gutenberg-Universität Mainz
Source Name: 
DIPC

Understanding the robustness of topological phases of
matter in the presence of strong interactions, and synthesising novel
strongly-correlated topological materials, lie among the most important and
difficult challenges of modern theoretical and experimental physics.

The synthetic Creutz-Hubbard ladder is a paradigmatic
model that provides a neat playground to address these challenges, including
the generation of flat bands as well as of non-doubled Dirac dispersion
relations.

   In [1], we
present a theoretical analysis of the competition between correlated
topological phases and orbital quantum magnetism in the regime of strong
interactions at half-filling.

   We predict
topological quantum phase transitions for weak and intermediate interactions
with different underlying conformal field theories (CFTs), i.e. Dirac versus
Majorana CFTs.

   In [2], we study
the response of an interacting system of Dirac-Weyl fermions confined in a
one-dimensional (1D) ring: we show that tuning of interactions leads to a
unique many-body system that displays either a suppression or an enhancement of
the Drude weight—the zero-frequency peak in the ac conductivity—with respect to
the non-interacting value.

   Both studies are
furthermore confirmed and extended by extensive numerical simulations based on
matrix product states (MPS) and binary Tree Tensor Networks (bTTN).

   Moreover we
propose how to experimentally realize this model in a synthetic ladder, made of
two internal states of ultracold fermionic atoms in a one-dimensional optical
lattice.

References:

[1] J. Jünemann, et al., PRX 7, 031057 (2017); [2] M.
Bischoff, et al., arXiv:1706.02679

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