Tensor Networks Can Resolve Fermi Surfaces

Abstract

We demonstrate that projected entangled-pair states (PEPS) are able to represent ground states of critical, fermionic systems exhibiting both 1d and 0d Fermi surfaces on a 2D lattice with an efficient scaling of the bond dimension. Extrapolating finite size results for the Gaussian restriction of fermionic projected entangled-pair states to the thermodynamic limit, the energy precision as a function of the bond dimension is found to improve as a power law, illustrating that an arbitrary precision can be obtained by increasing the bond dimension in a controlled manner. In this process, boundary conditions and system sizes have to be chosen carefully so that nonanalyticities of the Ansatz, rooted in its nontrivial topology, are avoided.

Small changes in correspondence to the PRL publication

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Cited by in corpus (15)

• Fermionic tensor network methods
• Generating function for projected entangled-pair states
• Continuous ferromagnetic quantum phase transition on an anisotropic Kondo lattice
• 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
• Fermionic Isometric Tensor Network States in Two Dimensions
• Chiral spin liquids with projected Gaussian fermionic entangled pair states
• Unveiling Correlated Two-dimensional Topological Insulators through Fermionic Tensor Network States -- Classification, Edge Theories and Variational Wavefunctions
• Efficient conversion from fermionic Gaussian states to matrix product states
• Finite-Entanglement Scaling of 2D Metals
• Constructive Fermionic Matrix Product States for Projected Fermi Sea
• Stacked tree construction for free-fermion projected entangled pair states
• Gaussian matrix product states cannot efficiently describe critical systems
• GCAMPS: A Scalable Classical Simulator for Qudit Systems