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arXiv:1909.00449 · Physical review. E

Thermal state entanglement entropy on a quantum graph

Alberto Verga, Ricardo Gabriel Elías

Published Dec 26, 2019• 5 citations
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Abstract

A particle jumps between the nodes of a graph interacting with local spins. We show that the entanglement entropy of the particle with the spin network is related to the length of the minimum cycle basis. The structure of the thermal state is reminiscent of the string net of spin liquids.
DOI
10.1103/physreve.100.062137

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Entanglement entropy is a powerful tool for characterizing spin liquids and other systems with long-range entanglement. For gapped spin liquids, this problem has been well-studied, finding a universal subleading constant term in the entanglement entropy, known as the topological entanglement entropy. In this paper, the idea of topological entanglement entropy is generalized to the gapless UUU(1) spin liquid. First, it is shown that the entanglement entropy separates into two pieces, one due to emergent charges of the theory (assumed to be gapped) and one due to the emergent gapless gauge mode. Both give universal subheading contributions to the entanglement entropy, which are logarithmic in the size of the region considered. The photon contribution is due to the local physics of the gapless mode. The particle contribution, on the other hand, is a topological term, generalizing the notion of topological entanglement entropy. A construction is presented which can isolate this topological piece by eliminating the photon contribution and other local terms, such as the area law. This topological term in the entanglement entropy can serve as a powerful diagnostic tool for UUU(1) spin liquids.
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