TY - JOUR
T1 - Entanglement spectrum of a topological phase in one dimension
AU - Pollmann, Frank
AU - Turner, Ari M.
AU - Berg, Erez
AU - Oshikawa, Masaki
PY - 2010/2/26
Y1 - 2010/2/26
N2 - We show that the Haldane phase of S=1 chains is characterized by a double degeneracy of the entanglement spectrum. The degeneracy is protected by a set of symmetries (either the dihedral group of π rotations about two orthogonal axes, time-reversal symmetry, or bond centered inversion symmetry), and cannot be lifted unless either a phase boundary to another, "topologically trivial," phase is crossed, or the symmetry is broken. More generally, these results offer a scheme to classify gapped phases of one-dimensional systems. Physically, the degeneracy of the entanglement spectrum can be observed by adiabatically weakening a bond to zero, which leaves the two disconnected halves of the system in a finitely entangled state.
AB - We show that the Haldane phase of S=1 chains is characterized by a double degeneracy of the entanglement spectrum. The degeneracy is protected by a set of symmetries (either the dihedral group of π rotations about two orthogonal axes, time-reversal symmetry, or bond centered inversion symmetry), and cannot be lifted unless either a phase boundary to another, "topologically trivial," phase is crossed, or the symmetry is broken. More generally, these results offer a scheme to classify gapped phases of one-dimensional systems. Physically, the degeneracy of the entanglement spectrum can be observed by adiabatically weakening a bond to zero, which leaves the two disconnected halves of the system in a finitely entangled state.
UR - http://www.scopus.com/inward/record.url?scp=77954821307&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.81.064439
DO - 10.1103/PhysRevB.81.064439
M3 - Article
AN - SCOPUS:77954821307
SN - 1098-0121
VL - 81
JO - Physical Review B - Condensed Matter and Materials Physics
JF - Physical Review B - Condensed Matter and Materials Physics
IS - 6
M1 - 064439
ER -