Topological order and reflection positivity
1 Harvard University - Cambridge, MA 02138, USA
2 Department of Physics, University of Basel - Basel, Switzerland
Received: 19 December 2013
Accepted: 11 February 2014
The focus of this paper is twofold. First, we observe that Hamiltonians displaying both topological order and reflection positivity have an interesting property: expectations in different ground-state vectors of a given local operator WA have the same sign. Secondly, we illustrate this result with a specific Majorana Hamiltonian, related to the toric code which is widely studied in quantum information theory. We show that expectations of reflection-symmetric loops in ground states of this Hamiltonian are vortex-free or vortex-full.
PACS: 03.65.-w – Quantum mechanics / 05.30.Fk – Fermion systems and electron gas / 05.30.Pr – Fractional statistics systems (anyons, etc.)
© EPLA, 2014