String-net liquid

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In

gauge group; or still more general networks.[1]

Overview

The string-net model is claimed to show the derivation of photons, electrons, and U(1) gauge charge, small (relative to the

Fermi statistics
). However, their model does not account for the
standard model
.

For strings labeled by the positive integers, string-nets are the

Fotini Markopoulou, Simone Severini argued that there are some similarities to spin networks (but not necessarily an exact equivalence) that gives rise to U(1) gauge charge and electrons in the string net mechanism.[4]

Herbertsmithite may be an example of string-net matter.[5][6]

Examples

Z2 spin liquid

Z2 spin liquid obtained using slave-particle approach may be the first theoretical example of string-net liquid.[7][8]

The toric code

The

boundary conditions with a spin-1/2 on each link. It can be shown that the ground-state of the standard toric code Hamiltonian is an equal-weight superposition of closed-string states.[9] Such a ground-state is an example of a string-net condensate[10] which has the same topological order
as the Z2 spin liquid above.

References

  1. S2CID 51962817
    .
  2. S2CID 117563047
    . loop quantum gravity appears to be a string net condensation ...
  3. arXiv:hep-th/0611197
    . We argue (but do not prove) that under certain conditions the spins in the system can arrange themselves in regular, lattice-like patterns at low temperatures.
  4. S2CID 6959359
    . The characterization of the string-condensed ground state is difficult but its excitations are expected to be that of a U(1) gauge theory, ... The two main differences between this model and the original string-net condensation model proposed by Levin and Wen are that in the present case the background lattice is dynamical and has hexagonal rather than square plaquettes.
  5. ^ Bowles, Claire. "Have researchers found a new state of matter?". Eureka Alert. Retrieved 29 January 2012.
  6. doi:10.1016/s0262-4079(07)60640-x
    . Retrieved 29 January 2012.
  7. PMID 10043303
    .
  8. ^ Xiao-Gang Wen, Mean Field Theory of Spin Liquid States with Finite Energy Gaps and Topological Orders, Phys. Rev. B44, 2664 (1991).
  9. arXiv:0904.2771 [cond-mat.mes-hall].{{cite arXiv}}: CS1 maint: multiple names: authors list (link
    )
  10. S2CID 118522495
    .
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