Alexander Nersesyan
(The Andronikashvili Institute of Physics)

Abstract:

A brief introduction to Abelian bosonization will be given with the scope of 3 lectures. The model that will be used to explain the idea and formalism of bosonization is the spin-1/2 XXZ spin chain. The lectures cover the following topics:

• XXZ spin-1/2 chain and its mapping onto spinless fermions via Jordan-Wigner transformation.

• Continuum limit, chiral fernions, emergent symmetries and conservation laws.

• U(1) Kac-Moody algebra of chiral currents and Tomonaga bosons.

• XXZ spin chain as a Tomonaga-Luttinger liquid.

• Field-theory formalism: fermion as a kink of a scalar field. Tomonaga-Luttinger liquid and the theory of a massless bosons.

• Bosonization of a massless fermion.

• Reduction of the XXZ spin chain to a quantum sine-Gordon model. Ground state phases of the model.

• Absence of fermionic quansiparticles in Tomonaga-Luttinger liquid.