Mortier Q, Li MH, Haegeman J, Bultinck N. Finite-Entanglement Scaling of 2D Metals.
PHYSICAL REVIEW LETTERS 2023;
131:266202. [PMID:
38215387 DOI:
10.1103/physrevlett.131.266202]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2023] [Revised: 09/27/2023] [Accepted: 11/21/2023] [Indexed: 01/14/2024]
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 L scales as S∼Llog[ξf(L/ξ)] in the optimal tensor network, and hence area-law entangled, state approximation to a metallic state, where f(x) is a scaling function which depends on the shape of the Fermi surface and ξ 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.
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