IFA Tutorials - Gergely Szirmai: 'Simulation of gauge theories on optical lattices I - External gauge fields'
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Koll. D, Math Department (1531-221)
Simulation of gauge theories on optical lattices I - External gauge fields
Gergely Szirmai, Institute for Solid State Physics and Optics, Wigner Research Centre for Physics
In this talk we discuss the motion of non-interacting ultracold fermions on 2-dimensional optical lattices subjected to artificial gauge fields. In particular, we examine the quantum Hall effect appearing in the presence of Abelian gauge potentials, like in the case of the motion of electrons in a homogeneous magnetic field. By changing the strength of the synthetic external gauge field the energy spectrum shows a fractal structure, which forms the celebrated Hofstadter butterfly. When the Fermi energy lies in a bulk gap the infinite sample is insulating, while a finite sample holds chiral edge state modes responsible for a quantized transverse conductivity. We also discuss non-Abelian gauge potentials and spin-orbit coupling, which can lead to the spin quantum Hall effect.