Vacuum degeneracy of chiral spin states in compactified space
Abstract
A chiral spin state is not only characterized by the T and P order parameter E123=S1.(S2×S3), it is also characterized by an integer k. In this paper we show that this integer k can be determined from the vacuum degeneracy of the chiral spin state on compactified spaces. On a Riemann surface with genus g the vacuum degeneracy of the chiral spin state is found to be 2kg. Among those vacuum states, some kg states have <E123>>0, while other kg states have <E123><0. The dependence of the vacuum degeneracy on the topology of the space reflects some sort of topological ordering in the chiral spin state. In general the topological ordering in a system is classified by topological theories.
- Publication:
-
Physical Review B
- Pub Date:
- October 1989
- DOI:
- 10.1103/PhysRevB.40.7387
- Bibcode:
- 1989PhRvB..40.7387W
- Keywords:
-
- 75.10.-b;
- 61.20.-p;
- 67.90.+z;
- General theory and models of magnetic ordering;
- Structure of liquids;
- Other topics in quantum fluids and solids;
- liquid and solid helium