Simulations of strongly correlated materials: Clusters and DMFT using a Lanczos solver
Simulations of strongly correlated materials: Clusters and DMFT using a Lanczos solver
The Hubbard model is the simplest many body Hamiltonian which describes the key elements of interacting electron systems: the kinetic energy and the electron-electron repulsion. We look at two methods that can reduce the infinite size of the Hubbard Hamiltonian. The first is to cut the lattice into...
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Personal Name(s): | Bugeanu, Mihaela Monica (Corresponding author) |
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Contributing Institute: |
GRS; GRS |
Imprint: |
2012
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Document Type: |
Report |
Subject (ZB): | |
Link: |
OpenAccess |
Publikationsportal JuSER |
The Hubbard model is the simplest many body Hamiltonian which describes the key elements of interacting electron systems: the kinetic energy and the electron-electron repulsion. We look at two methods that can reduce the infinite size of the Hubbard Hamiltonian. The first is to cut the lattice into finite clusters. A d-dimensional cluster will be defined by d vectors. Cutting off the infinite lattice introduces some artifacts of finite-size. We investigate in this thesis several properties that can help us choose a better combination of vectors. The squareness, the imperfection and bipartiteness are the most important of these. The squareness tells us how close the cluster is to a square one. The imperfection is a measure of the missing nearest neighbours of the finite lattice up to the highest ring available for that lattice. For a system of electrons, especially at half filling we have to keep track of the bipartiteness of the cluster to avoid frustration. A second way of reducing the size of the Hamiltonian is the dynamical mean field theory, mapping the Hamiltonian onto a site connected to a dynamical, non-interacting bath. In this thesis we introduce a new method of calculating the self consistent parameters of the bath. This method relies on preserving the moments of the Green function calculated using continued fractions. As am improvement to existing techniques the Green function is computed as one single continued fraction gaining access to twice as many moments as previous approaches. Both methods require solving a Hamiltonian to find its eigenvalues and eigenvectors. To do that we use the Lanczos algorithm which is a direct way of getting the ground state information. Our implementation combines the advantages of C++ as a fast high-level language and Lua a lightweight, interpreted one. We use Lua for setting up the single particle Hamiltonian and to call the C++ routines for the computationally intensive part of actually solving the many body Hamiltonian. We show how we can implement a simple interface between Lua and C++, gaining access from Lua to all the C++ classes and routines, while keeping the flexibility of a script language. |