Theoretical Physics Seminar: Konstantinos Meichanetzidis (Oxford)
From knots to spin models to tensor networks
Spin models are simplified models of complex systems,
which however can capture relevant physical behaviour
and even exhibit computational universality.
The partition function encodes properties of a model instance, and
even for very simple models, computing it is a hard counting problem.
In this work, we reduce this task into tensor network contraction and
we focus on the q-state Potts model. In particular, we evaluate the
partition function Z(q) of the q-state Potts model whose interaction pattern is
such that Z(q) is a knot invariant. The knot invariant we evaluate is the Jones polynomial,
which is a central quantity in the mathematical study of knots.
We benchmark our algorithm on a dataset of randomly generated knots and
show that for q<5 it shows improved asymptotic performance over the state of the art
using moderate computing resources.