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Finding the ground state of a lattice gauge theory with fermionic tensor networks: A 2+1d ℤ2 demonstration

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Emonts,  Patrick       
Theory, Max Planck Institute of Quantum Optics, Max Planck Society;
MCQST - Munich Center for Quantum Science and Technology, External Organizations;
IMPRS (International Max Planck Research School), Max Planck Institute of Quantum Optics, Max Planck Society;

Borla,  Umberto
Theory, Max Planck Institute of Quantum Optics, Max Planck Society;

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Citation

Emonts, P., Kelman, A., Borla, U., Moroz, S., Gazit, S., & Zohar, E. (2023). Finding the ground state of a lattice gauge theory with fermionic tensor networks: A 2+1d ℤ2 demonstration. Physical Review D, 107: 014505. doi:10.1103/PhysRevD.107.014505.


Cite as: https://hdl.handle.net/21.11116/0000-000B-EF53-B
Abstract
Tensor network states, and in particular Projected Entangled Pair States
(PEPS) have been a strong ansatz for the variational study of complicated
quantum many-body systems, thanks to their built-in entanglement entropy area
law. In this work, we use a special kind of PEPS - Gauged Gaussian Fermionic
PEPS (GGFPEPS) to find the ground state of $2+1d$ dimensional pure
$\mathbb{Z}_2$ lattice gauge theories for a wide range of coupling constants.
We do so by combining PEPS methods with Monte-Carlo computations, allowing for
efficient contraction of the PEPS and computation of correlation functions.
Previously, such numerical computations involved the calculation of the
Pfaffian of a matrix scaling with the system size, forming a severe bottleneck;
in this work we show how to overcome this problem. This paves the way for
applying the method we propose and benchmark here to other gauge groups, higher
dimensions, and models with fermionic matter, in an efficient,
sign-problem-free way.