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.
Highlights
Understanding the collective behavior of quantum manybody systems is a central theme in physics
Using these 2D numerical continuum tensor network states, we demonstrate how we can study fermionic physics in the continuum limit, applying the ansatz both to the challenging case of the free Fermi gas, as well as the attractive interacting Fermi gas in the unitary limit that can be realized in ultracold atom experiments
For the point η = −0.5 [Fig. 9(b)], the thermodynamic and continuum limits are rapidly approached as seen in both the TN and auxiliary field QMC (AFQMC) data; this is more challenging for the crossover point η = 1.0 [Fig. 9(b)] where there are sizable finite-size effects in both the TN and AFQMC results
Summary
Understanding the collective behavior of quantum manybody systems is a central theme in physics. The continuum description can be reached by taking the numerical limit of a set of tensor network states formulated on lattices with a discretization parameter , for → 0 This kind of numerical continuum MPS calculation has been demonstrated in conjunction with a variety of optimization algorithms [30,31,32]. The second is based on a combination of fermionic PEPS with a tree of isometries that successively coarse grains the continuum into discrete lattices Using these 2D numerical continuum tensor network states, we demonstrate how we can study fermionic physics in the continuum limit, applying the ansatz both to the challenging (for tensor networks) case of the free Fermi gas, as well as the attractive interacting Fermi gas in the unitary limit that can be realized in ultracold atom experiments.
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