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Numerical continuum tensor networks in two dimensions

Haghshenas, Reza and Cui, Zhi-Hao and Chan, Garnet Kin-Lic (2020) Numerical continuum tensor networks in two dimensions. . (Unpublished)

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We describe the use of tensor networks to numerically determine wave functions of interacting two-dimensional fermionic models in the continuum limit. We use two different tensor network states: one based on the numerical continuum limit of fermionic projected entangled pair states obtained via a tensor network formulation of multi-grid, and another based on the combination of the fermionic projected entangled pair state with layers of isometric coarse-graining transformations. We first benchmark our approach on the two-dimensional free Fermi gas then proceed to study the two-dimensional interacting Fermi gas with an attractive interaction in the unitary limit, using tensor networks on grids with up to 1000 sites.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Haghshenas, Reza0000-0002-5593-8915
Cui, Zhi-Hao0000-0002-7389-4063
Chan, Garnet Kin-Lic0000-0001-8009-6038
Additional Information:This work was supported by the US National Science Foundation (NSF) via grant CHE-1665333. GKC acknowledges support from the Simons Foundation via the Many-Electron Collaboration and via the Simons Investigator program. We have used the Uni10 library50 for implementation and PySCF51 to obtain benchmark data. We thank H. Shi, J. Drut, and T. Berkelbach for helpful discussions regarding the unitary Fermi gas.
Funding AgencyGrant Number
Simons FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20200923-104453194
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105489
Deposited By: Tony Diaz
Deposited On:23 Sep 2020 18:14
Last Modified:23 Sep 2020 18:14

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