Operator-Algebraic Renormalization of Fermionic Lattice Models.

Operator-Algebraic Renormalization of Fermionic Lattice Models.

Seminar author:Niklas Galke

Event date and time:03/10/2022 04:00:pm

Event location:GIQ & Zoom

Event contact:

[Zoom link]

An efficacious method for examining macroscopic phenomena in lattice models with many lattice points is the descripition in terms of an effective continuum theory. Different phases and corresponding critical points emerging as the density of points diverges can then be studied in the continuum limit. On the other hand, a limiting procedure that produces a continuum quantum field theory in a mathematically rigorous way is also interesting as a possibility of even defining the continuum theory from discrete QFT data in the first place. Goals are then to rigorously establish convergence and deduce error bounds. This is relevant, e.g., to the simulation of topological QFTs on quantum computers.

After reviewing the mathematical formulation of statistical theories in the language of C* algebras, we will discuss a general scheme for obtaining the continuum limit employing operator-algebraic methods. We will apply the procedure to spin systems and illustrate it by the special case of the transverse Ising chain and its conformal field theory, which can be handled by a quasi-free approach.