École Polytechnique Fédérale de Lausanne (EPFL), Institute of Physics, CH-1015 Lausanne, Switzerland
Center for Quantum Science and Engineering, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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Abstract
Through the introduction of auxiliary fermions, or an enlarged spin space, one can map local fermion Hamiltonians onto local spin Hamiltonians, at the expense of introducing a set of additional constraints. We present a variational Monte-Carlo framework to study fermionic systems through higher-dimensional ($gt$1D) Jordan-Wigner transformations. We provide exact solutions to the parity and Gauss-law constraints that are encountered in bosonization procedures. We study the $t$-$V$ model in 2D and demonstrate how both the ground state and the low-energy excitation spectra can be retrieved in combination with neural network quantum state ansatze.
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Cited by
[1] Filippo Vicentini, Damian Hofmann, Attila Szabó, Dian Wu, Christopher Roth, Clemens Giuliani, Gabriel Pescia, Jannes Nys, Vladimir Vargas-Calderon, Nikita Astrakhantsev, and Giuseppe Carleo, “NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems”, arXiv:2112.10526.
[2] Jannes Nys and Giuseppe Carleo, “Quantum circuits for solving local fermion-to-qubit mappings”, arXiv:2208.07192.
[3] Adam Wyrzykowski, “Local spin description of fermions on a lattice”, arXiv:2206.10393.
The above citations are from SAO/NASA ADS (last updated successfully 2022-10-14 22:03:06). The list may be incomplete as not all publishers provide suitable and complete citation data.
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This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.
