An area law for 2D frustration-free spin systems

Abstract: We prove that the entanglement entropy of the ground state of a locally gapped frustration-free 2D lattice spin system satisfies an area law with respect to a vertical bipartition of the lattice into left and right regions. We first establish that the ground state projector of any locally gapped frustration-free 1D spin system can be approximated to within error ∈ by a degree O(√nlog(∈-1)) (equation unformatted-refer to paper link) multivariate polynomial in the interaction terms of the Hamiltonian. This generalizes the optimal bound on the approximate degree of the boolean AND function, which corresponds to the special case of commuting Hamiltonian terms. For 2D spin systems we then construct an approximate ground state projector (AGSP) that employs the optimal 1D approximation in the vicinity of the boundary of the bipartition of interest. This AGSP has sufficiently low entanglement and error to establish the area law using a known technique.

Joint work with Itai Arad and David Gosset. arXiv: 2103.02492 (https://arxiv.org/abs/2103.02492)

quantum computing and information

Audience: researchers in the topic

( paper | video )

Comments: To request the zoom link, please send a message cqsiadmin@uts.edu.au using your business/organisation/institution email address. Hosted by Associate Professor Troy Lee, Centre for Quantum Software and Information, University of Technology Sydney

---

Centre for Quantum Software and Information Seminar Series

Series comments: To request the zoom link, please send a message to: cqsiadmin@uts.edu.au using your business/organisation/institution email address. Watch previous seminars on YouTube: - QSI Seminar Series 2021 (https://youtube.com/playlist?list=PLux7B14QYkPbDDOpqKSWScHXHodiBwr48) - QSI Seminar Series 2020 (https://youtube.com/playlist?list=PLux7B14QYkPZREUXReOq01ewLl02QXBXa)

---