# Lectures on the Physics of Strongly Correlated Systems

Magnetic phases of one-dimensional lattices with 2-4 fermions

At low energies, the dispersion relation is shown to be a linear function of the momentum. In the limit of weak interactions, the system is in the semi-metal phase. Siro and Harju (2012) T. Siro, A. Harju, Exact diagonalization of the Hubbard model on graphics processing units, Comp. Phys. Comm. 183 (2012) 1884 – 1889. Hubbard (1963) J. Hubbard, Electron correlations in narrow energy bands, Proc.

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Time evolution is implemented by the Krylov subspace method based on the Lanczos method [36–38]. These models give rise to pairing of holes and superconductivity in certain parameter ranges. Here we explore the changes in carrier effective mass and quasiparticle weight and in one- and two-particle spectral functions that occur in a dynamic Hubbard model upon pairing, by exact diagonalization of small systems.

## Perspectives from TDDFT and Green's Functions Karlsson, Da

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### Magnetic phases of one-dimensional lattices with 2-4 fermions

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Langdenheter tabell

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Triangular cluster
Exact diagonalization is a numerical technique used in physics to determine the eigenstates and energy eigenvalues of a quantum Hamiltonian. In this technique, a Hamiltonian for a discrete, finite system is expressed in matrix form and diagonalized using a computer. Exact diagonalization is only feasible for systems with a few tens of particles, due to the exponential growth of the Hilbert space dimension with the size of the quantum system. It is frequently employed to study
In this work, we apply the small crystal approach (SCA) to perform an exact diagonalization (ED) of the Hubbard Hamiltonian in order to obtain the full many-body descriptionoftheelectronicexcitationspectrumofAGNRsofdifferentwidths.TheSCAallows us to use a minimal number of sites to sample the most relevant k-points in the Brillouin
2011-02-19 · We take the Bose-Hubbard model to illustrate exact diagonalization techniques in a pedagogical way.

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### Hugo Strand - Institutionen för naturvetenskap och teknik

From these contexts, if infinite computational resources are permitted, the exact diago- An exact diagonalization package for a wide range of quantum lattice models (e.g. multi-orbital Hubbard model, Heisenberg model, Kondo lattice model). HΦ also supports the massively parallel computations.

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### Piotr Sierant - Google Scholar

We present results for ground-state properties of the two-dimensional 2D Hubbard model and an evaluation of the specific heat for the 1D and 2D Hubbard model. Using conservation laws (symmetries) for block-diagonalization.

## Johan Schött - Physicist - Orexplore LinkedIn

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