Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2011-03-28
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
7 pages, 2 figures. A presentation of this work can be found in the following talk at KITP: http://online.itp.ucsb.edu/online/
Scientific paper
We consider (2+1)-dimensional topological quantum states which possess edge states described by a chiral (1+1)-dimensional Conformal Field Theory (CFT), such as e.g. a general quantum Hall state. We demonstrate that for such states the reduced density matrix of a finite spatial region of the gapped topological state is a thermal density matrix of the chiral edge state CFT which would appear at the spatial boundary of that region. We obtain this result by applying a physical instantaneous cut to the gapped system, and by viewing the cutting process as a sudden "quantum quench" into a CFT, using the tools of boundary conformal field theory. We thus provide a demonstration of the observation made by Li and Haldane about the relationship between the entanglement spectrum and the spectrum of a physical edge state.
Katsura Hosho
Ludwig Andreas W. W.
Qi Xiao-Liang
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