Page 13 - Perimeter Institute 2012 Annual Report

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not be possible to predict the behaviour of a system from knowledge of its
parts – that is, there might be no path from bottom to top and the reductionist
approach would inevitably fail. This would explain why physicists have struggled
for decades to build effective theories of condensed matter phenomena based
on first principles. In particular, the exotic form of quantum matter known as
topologically ordered matter has been resistant to description via natural or
realistic Hamiltonians. (A Hamiltonian is a mathematical description of the way
a physical system changes.) Might topological order be strongly emergent?
Well, no. This year,
Perimeter Postdoctoral Researcher Lukasz Cincio
and
Perimeter Faculty member Guifre Vidal
were able to solve a model
of a system with emergent topological order, starting – at the bottom, as it
were – with only the microscopic description of the parts. Specifically, they
were able to start with a realistic Hamiltonian and show not only that the
system it describes is topologically ordered, but also numerically extract a
thorough characterization of that order. The researchers’ approach is valid
for other Hamiltonians as well – meaning that what they have developed
is a general method to compute the properties of emergent topological
order starting from microscopic descriptions only. They have, in short,
mapped a path from the bottom to the top.
References:
Proving the hologram:
S. Lee, “Background independent holographic description: From matrix field
theory to quantum gravity,”
JHEP
1210, 160 (2012), arXiv:1204:1780.
Reductionism vs. emergence:
L. Cincio and G. Vidal, “Characterizing topological order by studying the
ground states of an infinite cylinder,” arXiv:1208.2623.
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