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Register a new userFew-particle Greens functions for strongly correlated systems on infinite lattices
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Mona Berciu
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We show how few-particle Greens functions can be calculated efficiently for models with nearest-neighbor hopping, for infinite lattices in any dimension. As an example, for one dimensional spinless fermions with both nearest-neighbor and second nearest-neighbor interactions, we investigate the ground states for up to 5 fermions. This allows us not only to find the stability region of various bound complexes, but also to infer the phase diagram at small but finite concentrations.
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We introduce a new mathematical object, the fermionant ${mathrm{Ferm}}_N(G)$, of type $N$ of an $n times n$ matrix $G$. It represents certain $n$-point functions involving $N$ species of free fermions. When N=1, the fermionant reduces to the determinant. The partition function of the repulsive Hubbard model, of geometrically frustrated quantum antiferromagnets, and of Kondo lattice models can be expressed as fermionants of type N=2, which naturally incorporates infinite on-site repulsion. A computation of the fermionant in polynomial time would solve many interesting fermion sign problems.
It is shown that the Greens function on a finite lattice in arbitrary space dimension can be obtained from that of an infinite lattice by means of translation operator. Explicit examples are given for one- and two-dimensional lattices.
Two-particle Greens functions and the vertex functions play a critical role in theoretical frameworks for describing strongly correlated electron systems. However, numerical calculations at two-particle level often suffer from large computation time and massive memory consumption. We derive a general expansion formula for the two-particle Greens functions in terms of an overcomplete representation based on the recently proposed intermediate representation basis. The expansion formula is obtained by decomposing the spectral representation of the two-particle Greens function. We demonstrate that the expansion coefficients decay exponentially, while all high-frequency and long-tail structures in the Matsubara-frequency domain are retained. This representation therefore enables efficient treatment of two-particle quantities and opens a route to the application of modern many-body theories to realistic strongly correlated electron systems.
We reexamine the Yang-Yang-Takahashi method of deriving the thermodynamic Bethe ansatz equations which describe strongly correlated electron systems of fundamental physical interest, such as the Hubbard, $s-d$ exchange (Kondo) and Anderson models. It is shown that these equations contain some additional terms which may play an important role in the physics of the systems.
We adapt the Coupled Cluster Method to solid state strongly correlated lattice Hamiltonians extending the Coupled Cluster linear response method to the calculation of electronic spectra and obtaining the space-time Fourier transforms of generic Greens functions. We apply our method to the $MnO_2$ plane with orbital and magnetic ordering, to interpret electron energy loss experimental data, and to the Hubbard model, where we get insight into a possible pairing mechanism.
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