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Mapping local Hamiltonians of fermions to local Hamiltonians of spins

Verstraete, F. and Cirac, J. I. (2005) Mapping local Hamiltonians of fermions to local Hamiltonians of spins. Journal of Statistical Mechanics: Theory and Experiment, 2005 (9). Art. No. P09012. ISSN 1742-5468.

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We show how to map local fermionic problems onto local spin problems on a lattice in any dimension. The main idea is to introduce auxiliary degrees of freedom, represented by Majorana fermions, which allow us to extend the Jordan–Wigner transformation to dimensions higher than one. We also discuss the implications of our results in the numerical investigation of fermionic systems.

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Additional Information:© 2005 Institute of Physics and IOP Publishing Limited. Received 25 August 2005, accepted for publication 17 September 2005. Published 29 September 2005. We thank S Bravyi, J Preskill and G Vidal for discussions. After completion of this work, we became aware of the work by Ball [3], and we thank X Wen for bringing this work to our attention. This work was supported by the Gordon and Betty Moore Foundation, European projects CONQUEST, TOPQIP and QUPRODIS, and the DFG (SFB 631).
Subject Keywords:rigorous results in statistical mechanics, Hubbard model (theory), spin chains, ladders and planes (theory), density matrix renormalization group calculations
Issue or Number:9
Record Number:CaltechAUTHORS:VERjsmte05
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7188
Deposited By: Archive Administrator
Deposited On:16 Jan 2007
Last Modified:02 Oct 2019 23:39

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