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Title:
Universal lower bound on topological entanglement entropy
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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 on the lattice 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. In recent work, 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 which is invariant under constant-depth quantum circuits. Meanwhile, I will discuss the field-theoretic viewpoint on TEE, and I hope to foster some discussion comparing the lattice and the continuum. I believe there are many open questions here.
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