Fermionic matrix product states and one-dimensional topological phases

Autor(en)

Nick Bultinck, Dominic J. Williamson, Jutho Haegeman, Frank Verstraete

Abstrakt

We develop the formalism of fermionic matrix product states (fMPS) and show how irreducible fMPS fall in two different classes, related to the different types of simple Z(2) graded algebras, which are physically distinguished by the absence or presence of Majorana edge modes. The local structure of fMPS with Majorana edge modes also implies that there is always a twofold degeneracy in the entanglement spectrum. Using the fMPS formalism, we make explicit the correspondence between the Z(8) classification of time-reversal-invariant spinless superconductors and the modulo 8 periodicity in the representation theory of real Clifford algebras. Studying fMPS with general onsite unitary and antiunitary symmetries allows us to define invariants that label symmetry-protected phases of interacting fermions. The behavior of these invariants under stacking of fMPS is derived, which reveals the group structure of such interacting phases. We also consider spatial symmetries and show how the invariant phase factor in the partition function of reflection-symmetric phases on an unorientable manifold appears in the fMPS framework.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

Ghent University , Vienna Center for Quantum Science and Technology (VCQ)

Journal

Physical Review B

Band

95

Anzahl der Seiten

20

ISSN

1098-0121

DOI

https://doi.org/10.1103/PhysRevB.95.075108

Publikationsdatum

02-2017

Peer-reviewed

Ja

ÖFOS 2012

103015 Kondensierte Materie, 103024 Quantenfeldtheorie

ASJC Scopus Sachgebiete

Electronic, Optical and Magnetic Materials, Condensed Matter Physics

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/4081eb4d-2b9b-4b74-bfe8-c922ea73224b