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Tensor Networks Can Resolve Fermi Surfaces
Quinten Mortier1, Norbert Schuch2,3, Frank Verstraete1
1Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, 9000 Gent, Belgium.
Abstract:
We demonstrate that projected entangled-pair states 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.
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