{"id":1123,"date":"2017-12-13T22:22:52","date_gmt":"2017-12-13T20:22:52","guid":{"rendered":"https:\/\/webs.uab.cat\/giq\/seminar\/matrix-product-states-irreducible-forms-and-continuum-limits\/"},"modified":"2017-12-13T22:22:52","modified_gmt":"2017-12-13T20:22:52","slug":"matrix-product-states-irreducible-forms-and-continuum-limits","status":"publish","type":"seminar","link":"https:\/\/webs.uab.cat\/giq\/seminar\/matrix-product-states-irreducible-forms-and-continuum-limits\/","title":{"rendered":"Matrix Product States: Irreducible forms and Continuum limits"},"content":{"rendered":"<p>This talk will consist of two parts. In the first part,&nbsp;<br \/>\nI will present the irreducible form of a Matrix Product States (MPS),<br \/>\nwhich is a generalization of the canonical form of an MPS in the&nbsp;<br \/>\nsense that it is also defined for states with periodicity. I will&nbsp;<br \/>\nthen present a fundamental theorem for MPS in irreducible form,&nbsp;<br \/>\nnamely one that specifies how two tensors in irreducible form are&nbsp;<br \/>\nrelated if they give rise to the same MPS. Finally, I will present<br \/>\ntwo applications of this result: an equivalence between the&nbsp;<br \/>\nrefinement properties of a state and the divisibility properties&nbsp;<br \/>\nof its transfer matrix, and a more general characterisation of&nbsp;<br \/>\ntensors that give rise to matrix product states with symmetries.<br \/>\nIn the second part, I will present a study of continuum limits&nbsp;<br \/>\nof MPS, where we show that an MPS has a continuum limit (for a&nbsp;<br \/>\nproper definition thereof) if and only if its transfer matrix&nbsp;<br \/>\nis an infinitely divisible channel. We also consider continuum&nbsp;<br \/>\nlimits after a finite number of coarse graining steps, and&nbsp;<br \/>\ncharacterize it in terms of the divisibility properties of the&nbsp;<br \/>\ntransfer matrix. I will present several examples of states with&nbsp;<br \/>\nand without the two kinds of continuum limits.<\/p>\n<p>Joint work with I. Cirac, D. Perez-Garcia and N. Schuch.&nbsp;<br \/>\nBased on arXiv:1708.00880 and arxiv:1708.00029.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This talk will consist of two parts. In the first part,&nbsp; 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&nbsp; sense that it is also defined for states with periodicity. I will&nbsp; then present a fundamental theorem for MPS [&hellip;]<\/p>\n","protected":false},"author":20,"featured_media":0,"template":"","class_list":["post-1123","seminar","type-seminar","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/seminar\/1123","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/seminar"}],"about":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/types\/seminar"}],"author":[{"embeddable":true,"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/users\/20"}],"wp:attachment":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/media?parent=1123"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}