Topological Field Theory and Matrix Product States

DOI10.1103/PHYSREVB.96.075125arXiv1607.06766MaRDI QIDQ6275841

Minyoung You, Anton Kapustin, Alex Turzillo

Publication date: 22 July 2016

Abstract: It is believed that most (perhaps all) gapped phases of matter can be described at long distances by Topological Quantum Field Theory (TQFT). On the other hand, it has been rigorously established that in 1+1d ground states of gapped Hamiltonians can be approximated by Matrix Product States (MPS). We show that the state-sum construction of 2d TQFT naturally leads to MPS in their standard form. In the case of systems with a global symmetry $G$, this leads to a classification of gapped phases in 1+1d in terms of Morita-equivalence classes of $G$-equivariant algebras. Non-uniqueness of the MPS representation is traced to the freedom of choosing an algebra in a particular Morita class. In the case of Short-Range Entangled phases, we recover the group cohomology classification of SPT phases.

This page was built for publication: Topological Field Theory and Matrix Product States

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6275841)