Rigorous Free-Fermion Entanglement Renormalization from Wavelet Theory
Name
PhysRevX.8.011003.pdf
Size
1.33 MB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Haegeman, Jutho
Walter, Michael
Cotler, Jordan
Evenbly, Glen
Scholz, Volkher B.
Swingle, Brian Gordon
Date Issued
January 2018
Journal
Physical Review X
Publisher
American Physical Society
Citation
Haegeman, Jutho et al. "Rigorous Free-Fermion Entanglement Renormalization from Wavelet Theory." Physical Review X 8, 1 (January 2018): 011003
Version
Final published version
Abstract
We construct entanglement renormalization schemes that provably approximate the ground states of noninteracting-fermion nearest-neighbor hopping Hamiltonians on the one-dimensional discrete line and the two-dimensional square lattice. These schemes give hierarchical quantum circuits that build up the states from unentangled degrees of freedom. The circuits are based on pairs of discrete wavelet transforms, which are approximately related by a “half-shift”: translation by half a unit cell. The presence of the Fermi surface in the two-dimensional model requires a special kind of circuit architecture to properly capture the entanglement in the ground state. We show how the error in the approximation can be controlled without ever performing a variational optimization.
MIT Department
Massachusetts Institute of Technology. Department of Physics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1103/PhysRevX.8.011003
