Tensor networks can resolve Fermi surfaces

Mortier,  Quinten; Schuch, Norbert; Verstraete,  Frank; Haegeman,  Jutho

doi:10.1103/PhysRevLett.129.206401

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Tensor networks can resolve Fermi surfaces

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Schuch, Norbert
MCQST - Munich Center for Quantum Science and Technology, External Organizations;
Theory, Max Planck Institute of Quantum Optics, Max Planck Society;

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Citation

Mortier, Q., Schuch, N., Verstraete, F., & Haegeman, J. (2022). Tensor networks can resolve Fermi surfaces. Physical Review Letters, 129: 206401. doi:10.1103/PhysRevLett.129.206401.

Cite as: https://hdl.handle.net/21.11116/0000-000A-03FD-6

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 PEPS (GfPEPS) 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 non-analyticities of the GfPEPS, rooted in their
non-trivial topology, are avoided.