Speaker
Andrew Green
Description
Tensor networks embody deep insights about the
entanglement structure of many-body quantum systems. In
one dimension, they have led to algorithms that can
determine groundstates and follow time evolution with
remarkable precision. Entanglement is treated in a very
different way in field theories of quantum systems. These
are constructed in such a way that the saddle points do not
support entanglement – which is introduced by instanton or
fluctuation corrections.
We lift some of the insights about entanglement structure
from tensor networks to field theory. Our approach is to
explicitly construct a field integral for the partition function
over matrix product states, rather than coherent states. The
saddle points of such a theory support entanglement in a way
that bears interesting comparison with fluctuation and
instanton corrections to the usual field theory. In contrast to
numerical applications of tensor networks, where the bond
order is increased until a certain degree of accuracy is
attained, in this field theoretical application, qualitatively new
features appear even at low bond order. We demonstrate this
by discussing the field theory of certain deconfined quantum
critical points.
