ON-LINE TensorTalk: Matrix Product Unitaries
Speaker: Albert Werner
Title: Matrix Product Unitaries
Abstract;
Matrix product states are a successful tool for the to study and classification of one-dimensional quantum systems. In this talk, we will discuss a paper by Cirac et al. on the structure of Matrix Product Unitary operators (MPUs) which appear e.g. in the description of time evolutions of one-dimensional systems. Following [1], 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 for QCAs. If time permits, we also discuss the effect of symmetries on the MPU classification.
[1] https://arxiv.org/abs/1703.09188
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