Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Matrix Product Unitaries: Structure, Symmetries, and Topological
  Invariants   Matrix Product Vectors form the appropriate framework to study and classify
one-dimensional quantum systems. In this work, we develop the structure theory
of Matrix Product Unitary operators (MPUs) which appear e.g. in the description
of time evolutions of one-dimensional systems. We prove that all MPUs have a
strict causal cone, making them Quantum Cellular Automata (QCAs), and derive a
canonical form for MPUs which relates different MPU representations of the same
unitary through a local gauge. We use this canonical form to prove an Index
Theorem for MPUs which gives the precise conditions under which two MPUs are
adiabatically connected, providing an alternative derivation to that of
[Commun. Math. Phys. 310, 419 (2012), arXiv:0910.3675] for QCAs. We also
discuss the effect of symmetries on the MPU classification. In particular, we
characterize the tensors corresponding to MPU that are invariant under
conjugation, time reversal, or transposition. In the first case, we give a full
characterization of all equivalence classes. Finally, we give several examples
of MPU possessing different symmetries.

14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys