Description |
There are important models of quantum field theory, where the
configurations are divided into topological sectors. In these
models the topological susceptibility is a prominent, fully
non-perturbative observable.
We first discuss its definition, and its meaning in QCD and
in axion physics. Then we address the difficulty in its numerical
measurement. In this regard, we describe a new method - the
"slab method" - which is applicable even when the Monte Carlo
history is confined to a single topological sector. We present
results for the quantum rotor, the 2d Heisenberg model and
2-flavor QCD. In the latter case, a modern smoothing procedure
is involved, the Gradient Flow.
In the second part we focus on the Heisenberg model and the
millennium question whether or not its topological susceptibility
scales to a finite continuum limit. According to the paradigm
of the late 20th century this is not the case, which implies that
this famous model suffers from a conceptual disease. We have
revisited this issue by involving for the first time the
Gradient Flow, along with a powerful cluster algorithm.
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