Symmetries and boundary theories for chiral projected entangled pair states

Thorsten B. Wahl, Stefan T. Haßler, Hong-Hao Tu, J. Ignacio Cirac, and Norbert Schuch
Phys. Rev. B 90, 115133 – Published 19 September 2014

Abstract

We investigate the topological character of lattice chiral Gaussian fermionic states in two dimensions possessing the simplest descriptions in terms of projected entangled pair states (PEPS). They are ground states of two different kinds of Hamiltonians. The first one, Hff, is local, frustration free, and gapless. It can be interpreted as describing a quantum phase transition between different topological phases. The second one, Hfb, is gapped, and has hopping terms scaling as 1/r3 with the distance r. The gap is robust against local perturbations, which allows us to define a Chern number for the PEPS. As for (nonchiral) topological PEPS, the nontrivial topological properties can be traced down to the existence of a symmetry in the virtual modes that are used to build the state. Based on that symmetry, we construct stringlike operators acting on the virtual modes that can be continuously deformed without changing the state. On the torus, the symmetry implies that the ground state space of the local parent Hamiltonian is twofold degenerate. By adding a string wrapping around the torus, one can change one of the ground states into the other. We use the special properties of PEPS to build the boundary theory and show how the symmetry results in the appearance of chiral modes, and a universal correction to the area law for the zero Rényi entropy.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
7 More
  • Received 12 May 2014
  • Revised 25 August 2014

DOI:https://doi.org/10.1103/PhysRevB.90.115133

©2014 American Physical Society

Authors & Affiliations

Thorsten B. Wahl1,*, Stefan T. Haßler2, Hong-Hao Tu1, J. Ignacio Cirac1, and Norbert Schuch2

  • 1Max-Planck Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany
  • 2JARA Institute for Quantum Information, RWTH Aachen University, D-52056 Aachen, Germany

  • *thorsten.wahl@mpq.mpg.de

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 90, Iss. 11 — 15 September 2014

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review B

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×