Translation-symmetry protected topological orders on lattice

Details Translation-symmetry protected topological orders on lattice Translation-symmetry protected topological orders on lattice

2009-07-27

arxiv.org/abs/0907.4537v1

Physics

Condensed Matter

Strongly Correlated Electrons

Scientific paper

In this paper we systematically study a simple class of translation-symmetry protected topological orders in quantum spin systems using slave-particle approach. The spin systems on square lattice are translation invariant, but may break any other symmetries. We consider topologically ordered ground states that do not spontaneously break any symmetry. Those states can be described by Z2A or Z2B projective symmetry group. We find that the Z2A translation symmetric topological orders can still be divided into 16 sub-classes corresponding to 16 new translation-symmetry protected topological orders. We introduced four $Z_2$ topological indices $\zeta_{\v{k}}=0,1$ at $\v {k}=(0,0)$, $(0,\pi)$, $(\pi, 0)$, $(\pi ,\pi)$ to characterize those 16 new topological orders. We calculated the topological degeneracies and crystal momenta for those 16 topological phases on even-by-even, even-by-odd, odd-by-even, and odd-by-odd lattices, which allows us to physically measure such topological orders. We predict the appearance of gapless fermionic excitations at the quantum phase transitions between those symmetry protected topological orders. Our result can be generalized to any dimensions. We find 256 translation-symmetry protected Z2A topological orders for a system on 3D lattice.

Affiliated with

Also associated with

No associations

Rating

Translation-symmetry protected topological orders on lattice does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Translation-symmetry protected topological orders on lattice, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Translation-symmetry protected topological orders on lattice will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-245559