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Entanglement Entropy of Gapped Phases and Topological Order in Three dimensions | | Tarun Grover
; Ari M. Turner
; Ashvin Vishwanath
; | | Date: |
19 Aug 2011 | | Abstract: | We discuss entanglement entropy of gapped ground states in different
dimensions, obtained on partitioning space into two regions. For trivial phases
without topological order, we argue that the entanglement entropy may be
obtained by integrating an ’entropy density’ over the partition boundary that
admits a gradient expansion in the curvature of the boundary. This constrains
the expansion of entanglement entropy as a function of system size, and points
to an even-odd dependence on dimensionality. For example, in contrast to the
familiar result in two dimensions, a size independent constant contribution to
the entanglement entropy can appear for trivial phases in any odd spatial
dimension. We then discuss phases with topological entanglement entropy (TEE)
that cannot be obtained by adding local contributions. We find that in three
dimensions there is just one type of TEE, as in two dimensions, that depends
linearly on the number of connected components of the boundary (the ’zeroth
Betti number’). In D > 3 dimensions, new types of TEE appear which depend on
the higher Betti numbers of the boundary manifold. We construct generalized
toric code models that exhibit these TEEs and discuss ways to extract TEE in D
>=3. | | Source: | arXiv, 1108.4038 | | Services: | Forum | Review | PDF | Favorites | |
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