Description
We show how symmetries can lead to a dimensional reduction
and topological quantum orders and discuss the effects of
thermal fluctuations. We will
further show how exact dualities as well as duality
relations that appear only in a sector of certain theories
("emergent dualities") can be systematically derived. Our
method relies on the use of bond algebras wherein the
algebraic relations between all terms in the Hamiltonian are
examined. This method enables us to solve exactly several
quantum spin systems in high dimensions and to determine the
exact self dual points of all $Z_{N}$ lattice gauge theories
in 3+1 dimensions. Implications for quantum information will
be discussed.
Primary author
Prof.
Zohar Nussinov
(Washington university)
