Efficient calculation of real-space lattice propagators in the presence of a Fermi sea
Authors:
Oliver Tong,
Mona Berciu
Abstract:
We present an efficient method for computing the real-space propagators (lattice Green's functions) of any tight-binding Hamiltonian in the presence of a Fermi sea with carrier concentration $x$. The method is valid for any lattice, dispersion, and dimension, provided the corresponding $x=0$ propagators are known. We show that suitable combinations of the finite-$x$ particle-addition propagators h…
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We present an efficient method for computing the real-space propagators (lattice Green's functions) of any tight-binding Hamiltonian in the presence of a Fermi sea with carrier concentration $x$. The method is valid for any lattice, dispersion, and dimension, provided the corresponding $x=0$ propagators are known. We show that suitable combinations of the finite-$x$ particle-addition propagators have a real or imaginary part trivially related to their $x=0$ counterpart, while the remaining part follows from a Kramers-Kronig relation that can be evaluated for all energies at once using the fast Fourier transforms. The computational cost is therefore independent of the dimensionality, unlike that of direct Brillouin-zone integration. The particle-removal propagators follow from general identities. We validate the method against direct integration for hypercubic lattices in one, two, and three dimensions, and use the 2D square lattice to illustrate how the shape of the Fermi surface is imprinted on the spatial structure of the propagators. In particular, at energies far outside the band, the propagator maps converge to the Fraunhofer diffraction pattern whose aperture is the unoccupied part of the Brillouin zone.
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Submitted 18 August, 2026;
originally announced August 2026.
Extended Hubbard Model realized in 2D clusters of molecular anions
Authors:
Oliver Tong,
Katherine A. Cochrane,
Bingkai Yuan,
Tanya Roussy,
Mona Berciu,
Sarah A. Burke
Abstract:
The Hubbard model, despite its simplicity, is remarkably successful at describing numerous many-body phenomena. However, due to the small class of problems which can be solved exactly, there has been substantial interest in quantum simulations of extended Hubbard models to in turn, simulate materials and the interaction-driven phases they host. Here, we study small clusters of molecular anions of…
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The Hubbard model, despite its simplicity, is remarkably successful at describing numerous many-body phenomena. However, due to the small class of problems which can be solved exactly, there has been substantial interest in quantum simulations of extended Hubbard models to in turn, simulate materials and the interaction-driven phases they host. Here, we study small clusters of molecular anions of 3,4,9,10-perylene tetracarboxylic dianhydride on NaCl bilayers on Ag(111) using non-contact Atomic Force Microscopy, Electrostatic Force Spectroscopy, and Scanning Tunnelling Microscopy and Spectroscopy, and show that the occupation and transition energies are well described by an extended Hubbard model. In particular, asymmetric clusters of four molecules require the addition of differing inter-site electrostatic interaction terms and on-site potentials, as well as asymmetric hoping terms. With $t<<U$, occupation asymmetry is driven by these terms, independent of U. The good agreement between the model and the data indicate such molecular anion clusters could be used to probe larger systems and a more varied phase space of realistic fermionic Hubbard models.
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Submitted 6 September, 2025;
originally announced September 2025.