ON-LINE TensorTalk: Albert Werner

Speaker: Albert Werner

Title: Matrix Product Unitaries


We will continue our discussion 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. 

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Meeting ID: 661 6059 3115