Finite-Entanglement Scaling of 2D Metals

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 $S\sim L\log [\xi f(L/\xi )]$ 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 $\xi$ 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.

7 pages, 4 figures, 22 pages Supplemental Material Small changes in correspondence to the PRL publication

References in corpus (23)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Valence Bond Solids for Quantum Computation
• Scaling of entanglement support for Matrix Product States
• Matrix product states for critical spin chains: finite size scaling versus finite entanglement scaling
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• Fermionic Matrix Product States and One-Dimensional Topological Phases
• Universal tripartite entanglement in one-dimensional many-body systems
• Chiral central charge from a single bulk wave function
• Fermionic projected entangled-pair states and topological phases
• Finite correlation length scaling with infinite projected entangled pair states at finite temperature
• Symmetries and boundary theories for chiral Projected Entangled Pair States
• Multipartitioning topological phases by vertex states and quantum entanglement
• Finite-size and finite bond dimension effects of tensor network renormalization
• A universal tripartite entanglement signature of ungappable edge states
• A scaling hypothesis for projected entangled-pair states
• Local tensor network for strongly correlated projective states
• Matrix product states for Hartree-Fock-Bogoliubov wave functions
• Entanglement in tripartitions of topological orders: a diagrammatic approach
• U(1)-symmetric Gaussian fermionic projected entangled paired states and their Gutzwiller projection
• Projected d-wave superconducting state: a fermionic projected entangled pair state study
• Fermionic Gaussian PEPS in $3+1d$: Rotations and Relativistic Limits
• Gaussian matrix product states cannot efficiently describe critical systems

Cited by in corpus (4)

• Fermionic tensor network methods
• Efficient conversion from fermionic Gaussian states to matrix product states
• Finite-size scaling on the torus with periodic projected entangled-pair states
• Self-congruent point in critical matrix product states: An effective field theory for finite-entanglement scaling