Universal lower bound on topological entanglement entropy
- URL: http://arxiv.org/abs/2302.00689v2
- Date: Tue, 31 Oct 2023 22:32:17 GMT
- Title: Universal lower bound on topological entanglement entropy
- Authors: Isaac H. Kim, Michael Levin, Ting-Chun Lin, Daniel Ranard, Bowen Shi
- Abstract summary: Entanglement entropies of two-dimensional gapped ground states are expected to satisfy an area law.
In many models, the topological entanglement entropy (TEE) takes a universal value that characterizes the underlying topological phase.
However, the TEE is not truly universal: it can differ even for two states related by constant-depth circuits, which are necessarily in the same phase.
- Score: 11.62855746863658
- License: http://creativecommons.org/licenses/by-sa/4.0/
- Abstract: Entanglement entropies of two-dimensional gapped ground states are expected
to satisfy an area law, with a constant correction term known as the
topological entanglement entropy (TEE). In many models, the TEE takes a
universal value that characterizes the underlying topological phase. However,
the TEE is not truly universal: it can differ even for two states related by
constant-depth circuits, which are necessarily in the same phase. The
difference between the TEE and the value predicted by the anyon theory is often
called the spurious topological entanglement entropy. We show that this
spurious contribution is always nonnegative, thus the value predicted by the
anyon theory provides a universal lower bound. This observation also leads to a
definition of TEE that is invariant under constant-depth quantum circuits.
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