2016/07/31 by Johan Carlström · 11 citations
Physics and Astronomy · #Diagrammatic reasoning #Fermion #Hilbert space #Hubbard model #Lattice (music) #Nonlinear system #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #Quantum many-body systems #Spins #cond-mat.str-el #msc:82-08
paper · pdf · doi:10.1088/1361-648x/aa7e1b
published in Journal of Physics Condensed Matter 29(38), 385602 (IOP Publishing) · Published here http://iopscience.iop.org/article/10.1088/1361-648X/aa7e1b
openalex publication_date 2017/07/06 · openalex created_date 2017/07/14 · arxiv created 2018/03/12 · arxiv updated 2018/03/13 · openalex updated_date 2026/08/05
I derive a dual description of lattice fermions, specifically focusing on the t-J and Hubbard models, that allow diagrammatic techniques to be employed efficiently in the strongly correlated regime, as well as for systems with a restricted Hilbert space. These constructions are based on spin-charge transformation, where the lattice fermions of the original model are mapped onto spins and spin-less fermions. This mapping can then be combined with Popov-Fedotov fermionisation, where the spins are mapped onto lattice fermions with imaginary chemical potential. The resulting models do not contain any large expansion parameters, even for strongly correlated systems. Also, they exhibit dramatically smaller corrections to the density matrix from nonlinear terms in the Hamiltonian. The combination of these two properties means that they can be addressed with diagrammatic methods, including simulation techniques based on stochastic sampling of diagrammatic expansions.