TY - JOUR

T1 - Loop braiding statistics in exactly soluble three-dimensional lattice models

AU - Lin, Chien Hung

AU - Levin, Michael

N1 - Publisher Copyright:
© 2015 American Physical Society.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2015/7/8

Y1 - 2015/7/8

N2 - We construct two exactly soluble lattice spin models that demonstrate the importance of three-loop braiding statistics for the classification of three-dimensional gapped quantum phases. The two models are superficially similar: both are gapped and both support particlelike and looplike excitations similar to those of charges and vortex lines in a ℤ2 × ℤ2 gauge theory. Furthermore, in both models the particle excitations are bosons, and in both models the particle and loop excitations have the same mutual braiding statistics. The difference between the two models is only apparent when one considers the recently proposed three-loop braiding process in which one loop is braided around another while both are linked to a third loop. We find that the statistical phase associated with this process is different in the two models, thus proving that they belong to two distinct phases. An important feature of this work is that we derive our results using a concrete approach: we construct string and membrane operators that create and move the particle and loop excitations and then we extract the braiding statistics from the commutation algebra of these operators.

AB - We construct two exactly soluble lattice spin models that demonstrate the importance of three-loop braiding statistics for the classification of three-dimensional gapped quantum phases. The two models are superficially similar: both are gapped and both support particlelike and looplike excitations similar to those of charges and vortex lines in a ℤ2 × ℤ2 gauge theory. Furthermore, in both models the particle excitations are bosons, and in both models the particle and loop excitations have the same mutual braiding statistics. The difference between the two models is only apparent when one considers the recently proposed three-loop braiding process in which one loop is braided around another while both are linked to a third loop. We find that the statistical phase associated with this process is different in the two models, thus proving that they belong to two distinct phases. An important feature of this work is that we derive our results using a concrete approach: we construct string and membrane operators that create and move the particle and loop excitations and then we extract the braiding statistics from the commutation algebra of these operators.

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U2 - 10.1103/PhysRevB.92.035115

DO - 10.1103/PhysRevB.92.035115

M3 - Article

AN - SCOPUS:84937822303

VL - 92

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

SN - 1098-0121

IS - 3

M1 - 035115

ER -