Numerical continuum tensor networks in two dimensions

Abstract

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.

arXiv comment9 pages, 9 figures, sample source codes are available at https://github.com/rezah/cpeps

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• Density-Matrix Renormalization Group for Continuous Quantum Systems
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• Neuralized Fermionic Tensor Networks for Quantum Many-Body Systems