Finite-Entanglement Scaling of 2D Metals
arXiv:2305.02091 · doi:10.1103/PhysRevLett.131.266202
Abstract
We extend the study of finite-entanglement scaling from one-dimensional gapless models to two-dimensional systems with a Fermi surface. In particular, we show that the entanglement entropy of a contractible spatial region with linear size scales as in the optimal tensor network, and hence area-law entangled, state approximation to a metallic state, where is a scaling function which depends on the shape of the Fermi surface and is a finite correlation length induced by the restricted entanglement. Crucially, the scaling regime can be realized with numerically tractable bond dimensions. We also discuss the implications of the Lieb-Schultz-Mattis theorem at fractional filling for tensor network state approximations of metallic states.
arXiv comment7 pages, 4 figures, 22 pages Supplemental Material Small changes in correspondence to the PRL publication
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