Matrix Product Ansatz for Fermi Fields in One Dimension




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Amer Physical Soc


We present an implementation of a continuous matrix product state for two-component fermions in one dimension. We propose a construction of variational matrices with an efficient parametrization that respects the translational symmetry of the problem (without being overly constraining) and readily meets the regularity conditions that arise from removing the ultraviolet divergences in the kinetic energy. We test the validity of our approach on an interacting spin-1/2 system and observe that the ansatz correctly predicts the ground-state magnetic properties for the attractive spin-1/2 Fermi gas, including the phase-oscillating pair correlation function in the partially polarized regime.



Delta functions, Majorana, Fermions, Superconductivity

"We acknowledge discussions with J. I. Cirac and F. Verstraete and the hospitality of the KITP at UCSB where those took place (NSF Grant No. PHY05-51164). Funding for this work was provided by the University of Cincinnati and by the DARPA OLE program through ARO W911NF-07-1-0464; parallel computing resources were from the Ohio Supercomputer Center (OSC)."


©2015 American Physical Society