Matrix Product States: Irreducible forms and Continuum limits

Seminar date and time: 
Monday, 18 December, 2017 - 12:00
Gemma de las Cuevas

This talk will consist of two parts. In the first part, 
I will present the irreducible form of a Matrix Product States (MPS),
which is a generalization of the canonical form of an MPS in the 
sense that it is also defined for states with periodicity. I will 
then present a fundamental theorem for MPS in irreducible form, 
namely one that specifies how two tensors in irreducible form are 
related if they give rise to the same MPS. Finally, I will present
two applications of this result: an equivalence between the 
refinement properties of a state and the divisibility properties 
of its transfer matrix, and a more general characterisation of 
tensors that give rise to matrix product states with symmetries.
In the second part, I will present a study of continuum limits 
of MPS, where we show that an MPS has a continuum limit (for a 
proper definition thereof) if and only if its transfer matrix 
is an infinitely divisible channel. We also consider continuum 
limits after a finite number of coarse graining steps, and 
characterize it in terms of the divisibility properties of the 
transfer matrix. I will present several examples of states with 
and without the two kinds of continuum limits.

Joint work with I. Cirac, D. Perez-Garcia and N. Schuch. 
Based on arXiv:1708.00880 and arxiv:1708.00029.

Campus d'excel·lència internacional U A B