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While it is well known that three dimensional quantum many-body systems can support non-trivial braiding statistics between particle-like and loop-like excitations, or between two loop-like excitations, we argue that a more fundamental quantity is the statistical phase associated with braiding one loop $\alpha$ around another loop $\beta$, while both are linked to a third loop $\gamma$.
Y. Aharonov and D. Bohm, Phys. Rev. 115
1959
Earlier work this paper cites.
J. B. Kogut, Rev. Mod. Phys. 51
1979
Earlier work this paper cites.
K. S. Brown, Cohomology of groups
1982
Earlier work this paper cites.
J. M. Leinaas and J. Myrheim, Nuovo Cimento 37B
1984
Earlier work this paper cites.
M. G. Alford and F. Wilczek, Phys. Rev. Lett. 62
1985
Earlier work this paper cites.
L. M. Krauss and F. Wilczek, Phys. Rev. Lett. 62
1990
Earlier work this paper cites.
R. Dijkgraaf and E. Witten, Commun. Math. Phys. 129
1990
Earlier work this paper cites.
C. Aneziris, A. P. Balachandran, L. Kauffman, and A. M. Srivastava, Int. J. Mod. Phys. A 6
1991
Cited alongside, same era.
M. G. Alford, K.-M. Lee, J. March-Russell, and J. Preskill, Nucl. Phys. B 384
1992
Cited alongside, same era.
M. de Wild Propitius, Topological interactions in broken gauge theories
1995
Cited alongside, same era.
J. C. Baez, D. K. Wise, and A. S. Crans, Adv. Theor. Math. Phys. 11
2007
Cited alongside, same era.
M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82
2010
Cited alongside, same era.
F. Verstraete, J. I. Cirac, J. I. Latorre, E. Rico, and M. M. Wolf, Phys. Rev. Lett. 94
2010
Cited alongside, same era.
M. Levin and Z.-C. Gu, Phys. Rev. B 86
2012
Later among the works it cites.
X. Chen, Z.-C. Gu, Z.-X. Liu, and X.-G. Wen, Phys. Rev. B 87
2013
Later among the works it cites.
Y. Hu, Y. Wan, and Y.-S. Wu, Phys. Rev. B 87
2013
Later among the works it cites.
M. Cheng and Z.-C. Gu, Phys. Rev. Lett. 112
2014
Closest in time.
X. Chen, Y.-M. Lu, and A. Vishwanath, Nat. Commun. 5
2014
Closest in time.
C.-H. Lin and M. Levin, Phys. Rev. B 89
2014
Closest in time.
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L. Fidkowski and A. Kitaev, Phys. Rev. B 83
2011
Cited alongside, same era.
Our analysis can be straightforwardly extended to gauge theories with any finite Abelian gauge group G G ; we focus on G = ( ℤ N ) K G=(\mathbb{Z}_{N})^{K} primarily to simplify the discussion
Cited in the paper.
There is also another two-loop braiding process in which a small loop α \alpha braids around a large loop β \beta , in the same way that a particle braids around a loop. The statistical phase for this process is similar to ( 1
Cited in the paper.
We say that a multi-loop braiding process can be “smoothly” deformed into another process if we can interpolate between the two processes via a sequence of local changes to the worldsheets swept out by the loops. This sequence of local changes can be arbitrary except that the worldsheets of any two loops that are being braided around one another must stay far apart during every step
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The exchange statistics θ α , c \theta_{\alpha,c} also satisfies linearity relations which are analogues of ( 3
Cited in the paper.
See supplementary material for details
Cited in the paper.