4 research outputs found
Supersymmetric lattice fermions on the triangular lattice: superfrustration and criticality
We study a model for itinerant, strongly interacting fermions where a
judicious tuning of the interactions leads to a supersymmetric Hamiltonian. On
the triangular lattice this model is known to exhibit a property called
superfrustration, which is characterized by an extensive ground state entropy.
Using a combination of numerical and analytical methods we study various ladder
geometries obtained by imposing doubly periodic boundary conditions on the
triangular lattice. We compare our results to various bounds on the ground
state degeneracy obtained in the literature. For all systems we find that the
number of ground states grows exponentially with system size. For two of the
models that we study we obtain the exact number of ground states by solving the
cohomology problem. For one of these, we find that via a sequence of mappings
the entire spectrum can be understood. It exhibits a gapped phase at 1/4
filling and a gapless phase at 1/6 filling and phase separation at intermediate
fillings. The gapless phase separates into an exponential number of sectors,
where the continuum limit of each sector is described by a superconformal field
theory.Comment: 50 pages, 12 figures, 2 appendice
Structured matrix methods for a polynomial root solver using approximate greatest common divisor computations and approximate polynomial factorisations.
This thesis discusses the use of structure preserving matrix methods for the numerical
approximation of all the zeros of a univariate polynomial in the presence of
noise. In particular, a robust polynomial root solver is developed for the calculation
of the multiple roots and their multiplicities, such that the knowledge of the noise
level is not required. This designed root solver involves repeated approximate greatest
common divisor computations and polynomial divisions, both of which are ill-posed
computations. A detailed description of the implementation of this root solver is
presented as the main work of this thesis. Moreover, the root solver, implemented
in MATLAB using 32-bit floating point arithmetic, can be used to solve non-trivial
polynomials with a great degree of accuracy in numerical examples