Speaker
Ville Lahtinen
Description
We show that all so(N)1 universality class quantum
criticalities emerge when one-dimensional generalized cluster
models are perturbed with Ising or Zeeman terms. Each
critical point is described by a low-energy theory of N linearly
dispersing fermions, whose spectrum we show to precisely
match the prediction by so(N)1 conformal field theory.
Furthermore, by an explicit construction we show that all the
cluster models are dual to non-locally coupled transverse field
Ising chains, with the universality of the so(N)1 criticality
manifesting itself as N of these chains becoming critical. This
duality also reveals that the symmetry protection of cluster
models arises from the underlying Ising symmetries and it
enables the identification of local representations for the
primary fields of the so(N)1conformal field theories. For the
simplest and experimentally most realistic case that
corresponds to the original one-dimensional cluster model
with local three-spin interactions, our results show that the
su(2)2≃so(3)1 Wess-Zumino-Witten model can emerge in a
local, translationally invariant and Jordan-Wigner solvable
spin-1/2 model. Our results pave the way for classifying
criticalities between symmetry-protected topological states.
